A close-coiled helical spring with n coils, mean radius R and diameter d is subj

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Question
A close-coiled helical spring with n coils, mean radius R and diameter d is subjected to an axial load W. What is the compression in the spring?
Options
A.
B.
C.
D.

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UPSC Civil Service Exam Questions problems

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1. The graphical condition for equilibrium of concurrent forces is that
Options
A. both the force polygon and the funicular polygon must be closed figures
B. funicular polygon should be a closed figure
C. force polygon need not be a closed figure
D. force polygon should be a closed figure

2. Consider the following strengths of concrete :
1. Cube strength
2. Cylinder strength
3. Split-tensile strength
4. Modulus of rupture
The correct sequence in decreasing order of these strengths is
Options
A. 3, 4, 2, 1
B. 3, 4, 1, 2
C. 4, 3, 2, 1
D. 4, 3, 1, 2

4. A cylindrical shell made of mild steel plate of 100 cm diameter is to be subjected to an internal pressure of 10 kg/cm². If the material yields at 2000 kg/cm², assuming factor of safety as four and using maximum principal stress theory, thickness of the plate will be
Options
A. 5 mm
B. 10 mm
C. 15 mm
D. 20 mm

5. A particle of mass 3 kg moving in a straight line decelerates uniformly from a speed of 40 m/s to 20 m/s in a distance of 300 m. Before it comes to rest, it will travel a further distance pf
Options
A. 10 m
B. 20 m
C. 50 m
D. 100 m

6. The plastic modulus of a section is 5 x 10^-4m³. Its shape factor is 1.2 and the plastic moment capacity is 120 kNm. What is the value of the yield stress of the material?
Options
A. 100 N/mm²
B. 200 N/mm²
C. 240 N/mm²
D. 288 N/mm²

7. The figure refers to a channel section of uniform thickness of 1 cm used as a beam with the cross-sectional dimensions shown in cm units. If the Moment of Inertia of channel I_xx be equal to 246 cm⁴ and C be the shear centre, then the value of e in cm is equal to
Options
A. 1.5
B. 2.5
C. 2.25
D. 1.67

8. Consider the following statements :
1. An ascending gradient of 1 in 100 meets an ascending gradient of 1 in 120 to form a Valley curve.
2. A falling gradient of 1 in 25 meets a falling gradient of 1 in 50 to form a summit curve.
3. The length of summit curve is determined on the basis of head light sight distance.
Which one of the statements given above is/are correct?
Options
A. 1 and 2
B. 2 and 3
C. 1 and 3
D. 2 only

9. Activated sludge is the
Options
A. resultant sludge removable from the aeration unit
B. sludge settled in the humus tank
C. sludge in the secondary tank post-aeration rich in microbial mass
D. sludge.in the secondary tank post aeration, rich in nutrients.

10. The given figure shows gradually varied flow in an open channel with a beak in bed slope. Types of water surface profiles occurring from left to right are
Options
A. H₂ , S₃
B. H₂ , S₂
C. H₂ , M₂
D. H₃ , M₂

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