Contour Gradient from a Point on a Uniformly Inclined Surface From any chosen point on a surface with a given (uniform) inclination, how many distinct contour gradients (lines of constant slope) can be drawn through that point?

Introduction:A contour gradient is a ground line along which the slope (rise over horizontal run) remains constant. In route location and drainage design, engineers often need to trace such lines from a given point on a hillside to maintain a prescribed gradient for roads, canals, or pipelines.

Given Data / Assumptions:

• The surface has a uniform inclination (a plane surface).
• A prescribed gradient value is fixed (e.g., 1 in n).
• A specific starting point is chosen on the surface.

Concept / Approach:

On a plane surface, all lines making the same angle with the horizontal have the same slope magnitude. Through a given point of a plane, infinitely many straight lines can be drawn in different directions; among these, an indefinite set can maintain the same slope magnitude, although their directions differ. Hence, for a specified gradient magnitude on a uniformly inclined plane, there is not just one unique path—there are infinitely many possible contour gradients through the point.

Step-by-Step Solution:

Verification / Alternative check:

Graphically, equal-slope lines on a plane correspond to a family of straight lines; field setting with a clinometer can trace many such lines emanating from the same point.

Why Other Options Are Wrong:

(a) and (b) artificially restrict possibilities; (d) cannot hold since options are mutually exclusive; (e) is false because contour gradients are meaningful on uniform slopes.

Common Pitfalls:

Confusing “contour line” (constant elevation) with “contour gradient” (constant slope); assuming unique alignment when only slope magnitude is specified.

Final Answer:

An indefinite number of contour gradients are possible