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