Q: Automatic/dumpy level sensitivity: The radius of curvature of the arc of a bubble tube (spirit level) is generally kept approximately equal to which value to achieve suitable sensitivity in ordinary levelling?

Introduction / Context: The sensitivity of a bubble tube depends on the radius of curvature of its internal arc. A longer radius means a flatter arc and a more sensitive bubble (greater displacement per unit tilt). Survey instrument design balances sensitivity with practicality to allow stable, readable bubbles during field work. Given Data / Assumptions: Ordinary levelling (engineer’s/dumpy level) rather than high-precision geodetic levelling. Ambient field conditions (wind, vibration) require a practical bubble sensitivity. Graduations typically read to a few seconds of arc per division. Concept / Approach: Typical radii for general-purpose levels are about 10 m, yielding workable sensitivity without excessive bubble travel. More precise instruments may use longer radii (e.g., 25–50 m) for finer sensitivity, but the common teaching value for general use is 10 m. Step-by-Step Solution: 1) Recall relationship: bubble movement per tilt ∝ radius of curvature.2) Match ordinary field practice to ≈10 m radius.3) Select 10 m as the representative value. Verification / Alternative check: Instrument datasheets for standard dumpy levels cite bubble sensitivities consistent with ~10 m radii, whereas precise tilting levels reach higher radii values. Why Other Options Are Wrong: 25–100 m: correspond to more sensitive, specialized levels. 5 m: would be too short, producing an overly stiff (insensitive) bubble. Common Pitfalls: Assuming “more sensitive” is always better; too sensitive bubbles are hard to center outdoors. Final Answer: 10 m

Q: Angular form of slope correction: If θ is the ground slope angle and l is the measured sloping distance between two points, what is the correction to reduce l to horizontal length?

Introduction / Context: Slope measurements must be reduced to horizontal to compute plan distances and areas correctly. When the ground slope angle θ is known, the correction can be expressed in a compact trigonometric form useful for quick computations and field tables. Given Data / Assumptions: Slope distance measured along the ground = l. Ground makes an angle θ with the horizontal. We need the correction to subtract from l to obtain horizontal distance. Concept / Approach: The horizontal distance is D = l cos θ. The required correction c = l − D = l(1 − cos θ). Using the identity 1 − cos θ = 2 sin²(θ/2), we get c = 2l sin²(θ/2), which is convenient for small-angle work and matches series forms used in approximations. Step-by-Step Solution: 1) Start with D = l cos θ.2) Compute correction: c = l − l cos θ.3) Apply identity: 1 − cos θ = 2 sin²(θ/2).4) Hence c = 2l sin²(θ/2). Verification / Alternative check: For small θ, sin(θ/2) ≈ θ/2 (in radians), giving c ≈ 2l (θ²/4) = l θ²/2, consistent with the series c ≈ h²/(2l) when h ≈ l sin θ and θ is small. Why Other Options Are Wrong: 2l cos²(θ/2) and others do not reduce to l(1 − cos θ). l sin θ gives vertical difference, not the correction. Common Pitfalls: Subtracting the wrong component (vertical instead of horizontal). Final Answer: 2l sin²(θ/2)

Q: Levelling set-up for true difference in elevation: To obtain the most accurate true difference in elevation between points A and B using a single set-up (to eliminate collimation error), where should the level be placed?

Introduction / Context: Levelling aims to find the difference in elevation (ΔRL) between two points. Systematic errors—especially collimation (line-of-sight) error—can bias staff readings. A classic way to eliminate this error in a single set-up is to place the instrument equidistant from the two staffs. Given Data / Assumptions: Single set-up differential levelling between A and B. Collimation error is small but nonzero. Curvature and refraction are negligible over short, equal sight lengths. Concept / Approach: If the instrument is at the midpoint, the back sight (BS) and fore sight (FS) distances are equal. Collimation error produces the same additive error on both readings and cancels in the difference (BS − FS). Thus, ΔRL is free of that error without needing instrument adjustment. Step-by-Step Solution: 1) Set up the level exactly midway between A and B.2) Take BS on A and FS on B with equal sight lengths.3) Compute ΔRL = BS − FS; collimation error cancels. Verification / Alternative check: Reciprocal levelling over obstacles generalizes this idea by reversing positions to eliminate curvature/refraction over long spans. Why Other Options Are Wrong: Near A or B / any point: unequal sight lengths retain collimation error in ΔRL. Maximum staff reading point: irrelevant to error cancellation. Common Pitfalls: Ignoring equality of sight distances—roughly equal is not exact when high precision is required. Final Answer: at the exact mid point of A and B

Q: Theodolite terminology and faces: Choose the correct set of statements regarding a transit theodolite and the definitions of left face and right face during observation.

Introduction / Context: Correct nomenclature for theodolite parts and observation faces is essential for angle measurement protocols (e.g., double centering). A transit theodolite permits full rotation of the telescope about the horizontal axis, while ‘‘face left’’ and ‘‘face right’’ define the position of the vertical circle relative to the observer. Given Data / Assumptions: A standard transit theodolite is used. Observer identifies the side on which the vertical circle (vernier/plate) lies. No special instrument peculiarities are implied. Concept / Approach: A theodolite capable of reversing (transiting) the telescope in the vertical plane is called a transit. During any pointing, if the vertical circle is on the left of the telescope (as seen by the observer), the instrument is in face left; if on the right, it is in face right. Observations are commonly repeated on both faces to eliminate certain systematic errors. Step-by-Step Solution: 1) Verify the definition of ‘‘transit’’—telescope rotates in vertical plane.2) Define face left/right by the side of the vertical circle during sighting.3) All statements align; select the combined option. Verification / Alternative check: Field procedures for horizontal and vertical angles specify ‘‘FL’’ and ‘‘FR’’ sets to average out index errors, confirming the definitions’ importance. Why Other Options Are Wrong: ‘‘None of these’’ contradicts standard surveying terminology. Common Pitfalls: Mistaking the face definition by looking from the wrong side; always judge as viewed during observation. Final Answer: all the above

Q: Bowditch (compass) rule—departure corrections: For a closed traverse of perimeter L with closing error in departure ΔD, what is the correction to the departure of a side of length l according to Bowditch’s rule?

Introduction / Context: Traverse adjustment distributes the misclosure among sides in proportion to their “weights.” Bowditch’s rule (the compass rule) assumes that linear and angular errors are proportional to traverse lengths, making corrections to departures and latitudes proportional to side lengths. Given Data / Assumptions: Closed traverse with computed total departure misclosure ΔD (ΣD ≠ 0) and latitude misclosure ΔL (ΣL ≠ 0). Perimeter (total traverse length) = L; side length under correction = l. Ordinary plane surveying precision; no rigorous least-squares adjustment. Concept / Approach: Bowditch’s rule prescribes: Correction to departure of a side = −(l/L) × ΔD. Similarly, correction to latitude of a side = −(l/L) × ΔL. The negative sign indicates the correction is applied opposite to the sense of the misclosure so that the adjusted sums become zero. Step-by-Step Solution: 1) Compute ΔD = ΣD (unadjusted) and ΔL = ΣL.2) For each side of length li, compute corrections: CDi = −(li/L)ΔD; CLi = −(li/L)ΔL.3) Apply to each side’s departure/latitude and recompute to achieve ΣD = ΣL = 0. Verification / Alternative check: Check that ΣCD = −ΔD and ΣCL = −ΔL; if satisfied, the adjustment is internally consistent. Why Other Options Are Wrong: (L/l)ΔD and −(l²/L²)ΔD: not part of Bowditch proportionality. Same-sign correction: would worsen the misclosure. Equal corrections: ignores length weighting. Common Pitfalls: Forgetting the negative sign, leading to increased misclosure. Applying corrections to bearings instead of departures/latitudes. Final Answer: −(l/L) × ΔD

Question 1

The 'fix' of a plane table station with three known points, is bad if the plane table station lies

Accepted Answer

on the circumference of the circumscribing circle

Question 2

The main principle of surveying is to work

Accepted Answer

from whole to the part

Question 3

Keeping the instrument height as 1.5 m, length of staff 4 m, the slope of the ground as 1 in 10, the sight on the down-slope, must be less than

Accepted Answer

25 m

Question 4

Pick up the correct statement from the following :

Accepted Answer

the eyepiece plays no part in defining the line of sight

Question 5

If S is the length of a subchord and R is the radius of simple curve, the angle of deflection between its tangent and sub-chord, in minutes, is equal to

Accepted Answer

1718.9 S/R.

Question 6

The slope correction for a length of 30 m along a gradient of 1 in 20, is

Accepted Answer

3.75 cm

Question 7

Two concave lenses of 60 cm focal length are cemented on either side of a convex lens of 15 cm focal length. The focal length of the combination is

Accepted Answer

30 cm

Question 8

Plane-table (plan table) surveying: Identify the method of surveying in which field observations and map plotting proceed simultaneously in the field, so that the plan is drawn directly while sights are taken.

Accepted Answer

Introduction / Context: Surveying methods differ in how data are observed and how the final plan is produced. Some methods require returning to the office for plotting from field notes, whereas others allow plotting on the spot. Recognizing which technique combines observation and plotting in real time is fundamental in engineering surveying and site planning. Given Data / Assumptions: The question seeks the surveying method where observation and plotting are done together in the field. Standard equipment terms are used: plane table, alidade, trough compass, plumbing fork. No special geodetic corrections are implied; this is ordinary topographical/cadastral work. Concept / Approach: Plane-table (plan-table) surveying mounts a drawing board on a tripod, fixes a sheet to scale, and uses an alidade for sighting. Points are sighted and directly plotted by rays and distances (or by intersection/traversing), so the map grows as observations proceed, enabling instant checks and rapid small-scale mapping. Step-by-Step Solution: 1) Identify the requirement: simultaneous observation and plotting.2) Recall that plane-table work draws rays on the sheet during each sight.3) Conclude that plane-table surveying uniquely satisfies the requirement. Verification / Alternative check: Textbook procedures—radiation, intersection, traversing, and resection—are all executed directly on the board, confirming real-time plotting capability. Why Other Options Are Wrong: Chain/compass: observations are recorded in field books; plotting is done later in the office. Tacheometry: uses theodolite/stadia; again plotted later unless combined with a plane table. Plane alidade triangulation only: not a standard stand-alone method name. Common Pitfalls: Confusing tacheometric measurement with plane-table plotting; they can be combined, but the defining feature of simultaneous plotting belongs to the plane table. Final Answer: plan table surveying

Question 9

Theodolite traversing and plotting accuracy: Which method is considered the most reliable for plotting a theodolite traverse to minimize graphical error?

Accepted Answer

Introduction / Context: The graphical reliability of a traverse plot depends on how cumulative angular and linear errors propagate. Coordinate methods convert each traverse side to departures (eastings) and latitudes (northings) and plot stations by their coordinates, thus distributing errors rigorously and enabling checks like the closing error. Given Data / Assumptions: Closed or open theodolite traverse with measured bearings/angles and lengths. Standard plane surveying accuracy (not geodetic). Use of Bowditch (compass) or transit rule to adjust misclosure. Concept / Approach: With independent coordinates, each station's easting and northing are computed from an assumed origin and plotted independently, minimizing accumulation of graphical error from one side to the next. It is superior to consecutive plotting, which compounds small drafting inaccuracies side-by-side. Step-by-Step Solution: 1) Compute departures/latitudes for each side from adjusted bearings and lengths.2) Accumulate to obtain independent coordinates of each station.3) Plot each station directly by its coordinates; join in sequence. Verification / Alternative check: Closure checks (ΣD = 0, ΣL = 0 after adjustment) validate the plotted figure and expose blunders before drafting. Why Other Options Are Wrong: Included angles + scaling and tangent methods: convenient but prone to cumulative drafting error. Consecutive coordinates: still serial; less robust than independent coordinates. Chord-and-offset: not the standard for precise traverse plotting. Common Pitfalls: Plotting from leg to leg without a coordinate framework, which can magnify small protractor/scale errors. Final Answer: by independent co-ordinates of each station

Question 10

Slope correction in chaining: For end points with level difference h over a measured slope length l, the exact horizontal distance is √(l² − h²). Expanding in series gives the slope correction c ≈ (h² / 2l) + (h⁴ / 8l³) + … . The second term may be …

Accepted Answer

Introduction / Context: In chaining along a slope, the measured length l exceeds the horizontal distance D. Converting the sloping measurement to horizontal requires the slope correction. A series expansion allows us to judge when higher-order terms can be ignored without introducing significant error—a key consideration in ordinary engineering surveys. Given Data / Assumptions: Slope length l = 20 m (chain length or taped segment). Difference in level between the two ends = h. Horizontal distance D = √(l² − h²); slope correction c = l − D. Acceptable drafting/measurement error ~1 mm to a few mm. Concept / Approach: Binomial expansion: √(l² − h²) = l √(1 − (h²/l²)) ≈ l [1 − (h²)/(2l²) − (h⁴)/(8l⁴) …]. Thus c = l − D ≈ (h²)/(2l) + (h⁴)/(8l³) + … . The question seeks the threshold h below which the second term is negligible for l = 20 m. Step-by-Step Solution: 1) Second-term magnitude: t₂ = h⁴/(8 l³).2) For l = 20 m and h = 3 m: t₂ = 3⁴ / (8 × 20³) = 81 / (8 × 8000) ≈ 0.00127 m ≈ 1.3 mm.3) 1–2 mm is within ordinary field tolerance; hence t₂ is negligible.4) For smaller h (≤2 m), t₂ becomes even smaller, clearly negligible. Verification / Alternative check: Compare the first term for h = 3 m: (h²)/(2l) = 9 / 40 = 0.225 m; the second term is ~0.0013 m, i.e., <1% of the first term and within plotting tolerances. Why Other Options Are Wrong: 2 m, 1 m, 0.5 m, 0.25 m: all are acceptable but overly conservative; the question asks the value below which neglect is justified—3 m is the accepted classroom threshold for a 20 m length. Common Pitfalls: Using c ≈ l − l cos θ directly without assessing higher-order terms for steep slopes. Confusing slope length l with horizontal D when computing areas. Final Answer: 3 m

Question 11

Automatic/dumpy level sensitivity: The radius of curvature of the arc of a bubble tube (spirit level) is generally kept approximately equal to which value to achieve suitable sensitivity in ordinary levelling?

Accepted Answer

Introduction / Context: The sensitivity of a bubble tube depends on the radius of curvature of its internal arc. A longer radius means a flatter arc and a more sensitive bubble (greater displacement per unit tilt). Survey instrument design balances sensitivity with practicality to allow stable, readable bubbles during field work. Given Data / Assumptions: Ordinary levelling (engineer’s/dumpy level) rather than high-precision geodetic levelling. Ambient field conditions (wind, vibration) require a practical bubble sensitivity. Graduations typically read to a few seconds of arc per division. Concept / Approach: Typical radii for general-purpose levels are about 10 m, yielding workable sensitivity without excessive bubble travel. More precise instruments may use longer radii (e.g., 25–50 m) for finer sensitivity, but the common teaching value for general use is 10 m. Step-by-Step Solution: 1) Recall relationship: bubble movement per tilt ∝ radius of curvature.2) Match ordinary field practice to ≈10 m radius.3) Select 10 m as the representative value. Verification / Alternative check: Instrument datasheets for standard dumpy levels cite bubble sensitivities consistent with ~10 m radii, whereas precise tilting levels reach higher radii values. Why Other Options Are Wrong: 25–100 m: correspond to more sensitive, specialized levels. 5 m: would be too short, producing an overly stiff (insensitive) bubble. Common Pitfalls: Assuming “more sensitive” is always better; too sensitive bubbles are hard to center outdoors. Final Answer: 10 m

Question 12

Angular form of slope correction: If θ is the ground slope angle and l is the measured sloping distance between two points, what is the correction to reduce l to horizontal length?

Accepted Answer

Introduction / Context: Slope measurements must be reduced to horizontal to compute plan distances and areas correctly. When the ground slope angle θ is known, the correction can be expressed in a compact trigonometric form useful for quick computations and field tables. Given Data / Assumptions: Slope distance measured along the ground = l. Ground makes an angle θ with the horizontal. We need the correction to subtract from l to obtain horizontal distance. Concept / Approach: The horizontal distance is D = l cos θ. The required correction c = l − D = l(1 − cos θ). Using the identity 1 − cos θ = 2 sin²(θ/2), we get c = 2l sin²(θ/2), which is convenient for small-angle work and matches series forms used in approximations. Step-by-Step Solution: 1) Start with D = l cos θ.2) Compute correction: c = l − l cos θ.3) Apply identity: 1 − cos θ = 2 sin²(θ/2).4) Hence c = 2l sin²(θ/2). Verification / Alternative check: For small θ, sin(θ/2) ≈ θ/2 (in radians), giving c ≈ 2l (θ²/4) = l θ²/2, consistent with the series c ≈ h²/(2l) when h ≈ l sin θ and θ is small. Why Other Options Are Wrong: 2l cos²(θ/2) and others do not reduce to l(1 − cos θ). l sin θ gives vertical difference, not the correction. Common Pitfalls: Subtracting the wrong component (vertical instead of horizontal). Final Answer: 2l sin²(θ/2)

Question 13

Levelling set-up for true difference in elevation: To obtain the most accurate true difference in elevation between points A and B using a single set-up (to eliminate collimation error), where should the level be placed?

Accepted Answer

Introduction / Context: Levelling aims to find the difference in elevation (ΔRL) between two points. Systematic errors—especially collimation (line-of-sight) error—can bias staff readings. A classic way to eliminate this error in a single set-up is to place the instrument equidistant from the two staffs. Given Data / Assumptions: Single set-up differential levelling between A and B. Collimation error is small but nonzero. Curvature and refraction are negligible over short, equal sight lengths. Concept / Approach: If the instrument is at the midpoint, the back sight (BS) and fore sight (FS) distances are equal. Collimation error produces the same additive error on both readings and cancels in the difference (BS − FS). Thus, ΔRL is free of that error without needing instrument adjustment. Step-by-Step Solution: 1) Set up the level exactly midway between A and B.2) Take BS on A and FS on B with equal sight lengths.3) Compute ΔRL = BS − FS; collimation error cancels. Verification / Alternative check: Reciprocal levelling over obstacles generalizes this idea by reversing positions to eliminate curvature/refraction over long spans. Why Other Options Are Wrong: Near A or B / any point: unequal sight lengths retain collimation error in ΔRL. Maximum staff reading point: irrelevant to error cancellation. Common Pitfalls: Ignoring equality of sight distances—roughly equal is not exact when high precision is required. Final Answer: at the exact mid point of A and B

Question 14

Theodolite terminology and faces: Choose the correct set of statements regarding a transit theodolite and the definitions of left face and right face during observation.

Accepted Answer

Introduction / Context: Correct nomenclature for theodolite parts and observation faces is essential for angle measurement protocols (e.g., double centering). A transit theodolite permits full rotation of the telescope about the horizontal axis, while ‘‘face left’’ and ‘‘face right’’ define the position of the vertical circle relative to the observer. Given Data / Assumptions: A standard transit theodolite is used. Observer identifies the side on which the vertical circle (vernier/plate) lies. No special instrument peculiarities are implied. Concept / Approach: A theodolite capable of reversing (transiting) the telescope in the vertical plane is called a transit. During any pointing, if the vertical circle is on the left of the telescope (as seen by the observer), the instrument is in face left; if on the right, it is in face right. Observations are commonly repeated on both faces to eliminate certain systematic errors. Step-by-Step Solution: 1) Verify the definition of ‘‘transit’’—telescope rotates in vertical plane.2) Define face left/right by the side of the vertical circle during sighting.3) All statements align; select the combined option. Verification / Alternative check: Field procedures for horizontal and vertical angles specify ‘‘FL’’ and ‘‘FR’’ sets to average out index errors, confirming the definitions’ importance. Why Other Options Are Wrong: ‘‘None of these’’ contradicts standard surveying terminology. Common Pitfalls: Mistaking the face definition by looking from the wrong side; always judge as viewed during observation. Final Answer: all the above

Question 15

Bowditch (compass) rule—departure corrections: For a closed traverse of perimeter L with closing error in departure ΔD, what is the correction to the departure of a side of length l according to Bowditch’s rule?

Accepted Answer

Introduction / Context: Traverse adjustment distributes the misclosure among sides in proportion to their “weights.” Bowditch’s rule (the compass rule) assumes that linear and angular errors are proportional to traverse lengths, making corrections to departures and latitudes proportional to side lengths. Given Data / Assumptions: Closed traverse with computed total departure misclosure ΔD (ΣD ≠ 0) and latitude misclosure ΔL (ΣL ≠ 0). Perimeter (total traverse length) = L; side length under correction = l. Ordinary plane surveying precision; no rigorous least-squares adjustment. Concept / Approach: Bowditch’s rule prescribes: Correction to departure of a side = −(l/L) × ΔD. Similarly, correction to latitude of a side = −(l/L) × ΔL. The negative sign indicates the correction is applied opposite to the sense of the misclosure so that the adjusted sums become zero. Step-by-Step Solution: 1) Compute ΔD = ΣD (unadjusted) and ΔL = ΣL.2) For each side of length li, compute corrections: CDi = −(li/L)ΔD; CLi = −(li/L)ΔL.3) Apply to each side’s departure/latitude and recompute to achieve ΣD = ΣL = 0. Verification / Alternative check: Check that ΣCD = −ΔD and ΣCL = −ΔL; if satisfied, the adjustment is internally consistent. Why Other Options Are Wrong: (L/l)ΔD and −(l²/L²)ΔD: not part of Bowditch proportionality. Same-sign correction: would worsen the misclosure. Equal corrections: ignores length weighting. Common Pitfalls: Forgetting the negative sign, leading to increased misclosure. Applying corrections to bearings instead of departures/latitudes. Final Answer: −(l/L) × ΔD

Question 16

Closed traverse with missing data: In a closed traverse, which of the following can be computed from the remaining measurements when one element is omitted?

Accepted Answer

Introduction / Context: A closed traverse geometrically returns to its starting point. This closure condition enables recovery of missing data using coordinate computations when one side’s measurements are lost or omitted, provided the rest are reliable. Given Data / Assumptions: Closed traverse with n sides; all sides except one have known lengths and bearings. Plane surveying assumptions; no geodetic curvature corrections needed for short traverses. Measurements are internally consistent or adjusted. Concept / Approach: Compute departures (D) and latitudes (L) of all known sides. Because ΣD = 0 and ΣL = 0 for a closed traverse, the unknown side must supply departures and latitudes equal to the negative of the sums of the known sides. From these (Du, Lu), compute the unknown length and bearing: length = √(Du² + Lu²) and bearing = arctan(Du/Lu) adjusted to the proper quadrant. Step-by-Step Solution: 1) Calculate Di, Li for known sides.2) Find Du = −ΣDknown, Lu = −ΣLknown.3) Compute length and bearing of the missing side from Du, Lu. Verification / Alternative check: Plotting the traverse by independent coordinates will visually confirm that the computed side closes the figure accurately. Why Other Options Are Wrong: Stating only length or only bearing underuses the closure conditions; both are determinable. Adjacent-side data alone are unnecessary if the rest of the traverse is known. ‘‘All the above’’ is incorrect because the single best statement is that both length and bearing can be found. Common Pitfalls: Forgetting quadrant corrections when deriving bearings from departures/latitudes. Final Answer: both length and bearing of one side

Question 17

Theodolite components and functions: Select the correct consolidated statement regarding the tangent screw, the levelling head (tribrach), and the levelling screws used to set the vertical rotation axis.

Accepted Answer

Introduction / Context: Accurate angle measurement requires correct instrument set-up: centering, levelling, and precise pointing. Understanding the function of the tangent screw, tribrach (levelling head), and levelling screws ensures repeatable, high-quality observations with theodolites and total stations. Given Data / Assumptions: Standard theodolite/total station mounted on a tripod. Normal field procedures: coarse clamping, fine pointing, and levelling. Vertical axis must be truly vertical to avoid angular errors. Concept / Approach: The tangent screw provides fine, controlled motion after clamping to precisely bisect targets. The instrument sits on the levelling head (tribrach), which carries the foot- (levelling) screws. By manipulating the levelling screws, the plate is tilted so that the instrument’s rotation axis becomes truly vertical, verified by the circular or tubular bubble. Step-by-Step Solution: 1) Clamp the motion; use tangent screw for fine sighting.2) Mount on tribrach; center over station via optical plummet.3) Level with the three/four foot screws to align the vertical axis. Verification / Alternative check: Two-peg test and face-left/face-right observations will expose mislevel or collimation issues, emphasizing correct use of these components. Why Other Options Are Wrong: ‘‘None of these’’ contradicts standard instrument anatomy and procedure. Common Pitfalls: Attempting fine pointing without clamping first, causing backlash effects. Levelling with only two screws rather than using the proper opposing-screw technique. Final Answer: all the above

Question 18

Levelling instruments — identify the condition(s) under which the sensitiveness of a spirit level tube (bubble tube) decreases, considering radius of curvature, tube diameter, bubble length, viscosity, and surface tension.

Accepted Answer

Introduction / Context:In surveying and civil engineering, the spirit level (bubble tube) on a level or theodolite is designed to be sensitive so that a very small tilt of the instrument results in a noticeable movement of the bubble. Understanding what parameters increase or decrease the sensitiveness (ability to respond to small angular changes) helps in instrument selection, maintenance, and calibration. Given Data / Assumptions: Sensitivity relates to the angular tilt required to move the bubble by one division. Tube geometry: radius of curvature (R), internal diameter, and bubble length. Fluid properties: viscosity (μ) and surface tension (σ) of the liquid in the tube. Concept / Approach: A more sensitive level shows more bubble movement for a tiny angular tilt. Geometrically, a larger radius of curvature (flatter arc) and a suitably long bubble generally increase sensitiveness, because the bubble shifts more per unit tilt. However, fluid-dynamic factors also matter: high viscosity and high surface tension resist bubble motion and slow the response, effectively reducing sensitiveness during practical use and adjustment. Step-by-Step Solution: 1) Geometric influence: increasing R (flatter tube) lowers the angle per division, enhancing sensitivity; increasing bubble length often increases responsiveness up to a limit.2) Diameter influence: its effect is secondary and design-dependent; larger diameter can reduce capillary restraint, often improving sensitivity, not decreasing it.3) Fluid properties: higher μ and σ impede bubble mobility, making the level less responsive to small tilts.4) Therefore, sensitiveness decreases when viscosity and surface tension are both increased. Verification / Alternative check: Instrument design texts note that for fast, sensitive bubbles, low-viscosity liquids and controlled wetting (surface tension) are preferred. Temperature control is also used to stabilize μ and σ during calibration. Why Other Options Are Wrong: Radius increased — generally increases sensitivity (opposite effect).Diameter increased — design-specific; often improves rather than reduces sensitivity.Bubble length increased — typically increases sensitivity up to design limits. Common Pitfalls: Confusing static geometric sensitivity with dynamic response; overlooking that fluid properties can dominate user-perceived sensitivity even if geometric sensitivity is high. Final Answer: both viscosity and surface tension are increased

Question 19

Chain surveying — the limiting (maximum) usable length of an offset does not depend on which of the following factors during field work and plotting?

Accepted Answer

Introduction / Context:Offsets are short measurements taken at right angles (or with set squares/cross-staffs) from a chain line to locate details such as boundaries, buildings, or fence lines. The limiting length of an offset is the longest offset that can be measured and plotted without exceeding allowable positional error. Knowing what controls this limit is vital for planning chain lines and ensuring accurate plans. Given Data / Assumptions: Error tolerance is set by required accuracy for the work. Instrument/method used to set perpendiculars affects angular error. Chosen map scale of plotting converts ground errors to plan errors. Concept / Approach: The maximum offset length is governed by the combined effect of (1) scale (smaller scales permit less ground error for a given plan error), (2) desired accuracy, and (3) the angular accuracy of the method used to set perpendiculars (e.g., optical square vs. cross-staff). Whether a feature is definite or indefinite (e.g., a hedge line with fuzzy edges) influences how you identify the feature but does not mathematically limit the offset length dictated by precision and scale. Step-by-Step Solution: 1) Establish permissible plan error from the scale and required accuracy.2) Translate to ground tolerance and relate to offset length.3) Recognize that better perpendicular-setting methods allow longer offsets for the same tolerance.4) Conclude that feature definiteness does not directly govern limiting length. Verification / Alternative check: Surveying manuals tabulate limiting offset lengths as functions of scale and instrument used, confirming dependence on accuracy and method, not on feature definiteness. Why Other Options Are Wrong: Accuracy — directly sets allowable error, thus affects the limit.Method of setting out perpendiculars — governs angular error, hence the limit.Scale of plotting — converts ground error to plan error and thus controls the limit. Common Pitfalls: Letting indistinct features drive offset length instead of improving feature definition (e.g., by supplementary ties) within the proper offset limit. Final Answer: indefinite features to be surveyed

Question 20

Geometrical optics — for a thin convex lens of focal length f, if f₁ and f₂ are the distances from the optical centre to two conjugate points P₁ and P₂ respectively, which relationship is correct?

Accepted Answer

none of these

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