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. If both Assertion and Reason are true and the Reason is the correct explanation of the Assertion.
• B. If both Assertion and Reason are true but the Reason is not the correct explanation of the Assertion.
• C. If Assertion is true but Reason is false.
• D. If both Assertion and Reason are false.

Answer 1

Answer: (B)

At the point of a rough contact where slipping is about to occur, the two forces acting on each object are normal reaction $N$ and frictional force $\mu N$.
Thus, limiting angle

$\tan \lambda =\frac{\mu N}{N}=\mu$
or $\lambda ={\tan }^{-1}(\mu )$ ... (i)
Now, at the point of sliding down the angle of inclination of the plane with the horizontal is called the angle of repose $(\alpha )$.
From figure

$\mu mg\cos \alpha =mg\sin \alpha$
or $\tan \alpha =\mu$
or $\alpha ={\tan }^{-1}(\mu )$ ... (ii)
From Eqs. (i) and (ii)
$\lambda =\alpha$