Question

Assertion Angle of repose is equal to the angle of limiting friction.
Reason When the body is just at the point of motion, the force of friction in this stage is called limiting friction.

• A. Both assertion and reason are true and reason is the correct explanation of assertion.
• B. Both assertion and reason are true but reason is not the correct explanation of assertion
• C. Assertion is true but reason is false.
• D. Both assertion and reason are false

Answer 1

Answer: (B)

The maximum value of static friction up to which body does not move is called limiting friction. Angle of repose is defined as the angle of the inclined plane with horizontal such that a body placed on it is just begins to slide. In limiting condition,
$F = mg \sin \alpha$ and $R = mg \cos \alpha$
Where $\alpha=$ angle of repose.
So $\frac{ F }{ R }=\tan \alpha$
$\therefore \frac{ F }{ R }=\mu_{ s }=\tan \theta=\tan \alpha\left(\because \tan \theta=\mu_{ s }\right)$
or $\theta=\alpha$