The angle of inclination of the plane at which a body begins to move down the plane is called:

Asked in SSC JE 03/03/2017 (Morning)

Detailed Explanation

Place a block on a board and slowly tilt the board. Up to some angle the block stays put; just beyond it, the block slides.

At the point of sliding: \( W\sin\alpha = \mu W\cos\alpha \Rightarrow \tan\alpha = \mu = \tan\phi \Rightarrow \alpha = \phi \)

Why “Angle of repose” Is Correct

The largest inclination at which the body stays at rest, i.e. the angle at which it just begins to slide down, is called the angle of repose. As the working shows, it is numerically equal to the angle of friction φ — but the name for the inclination of the plane is angle of repose, option (c).

Block of weight W on a rough plane inclined at α. Down the plane acts W sin α; the normal reaction is R = W cos α; friction F acts up the plane. As α is increased, sliding just begins when W sin α = μ W cos α, i.e. tan α = μ = tan φ. That limiting inclination is the angle of repose, and it equals the angle of friction φ.

Why the Other Options Are Wrong

A. Angle of friction: The angle of friction is the angle between the normal reaction and the resultant reaction; it is equal in value but is not the name of the plane's inclination.
B. Angle of projection: The angle of projection relates to projectiles.
D. None of these: Angle of repose is the correct term and is listed.

Key Point

Angle of repose = angle of friction φ (tan φ = μ).

Key Concepts for Students

Dry sand piles up at its angle of repose (about 30°–35°).
A body on a plane steeper than φ slides without any push.
Force to drag a body up a rough incline increases with μ.

Practice more: this is question 3 in Friction MCQs – Part 1. Try the whole set and check every answer instantly.