Question

A block of mass m rests on a rough inclined plane. The coefficient of friction between the surface and the block is $\mu$. At what angle of inclination $\theta$of the plane to the horizontal will the block just start to slide down the plane?

• A. $\theta = \tan^{- 1}\mu$
• B. $\theta = \cos^{- 1}\mu$
• C. $\theta = \sin^{- 1}\mu$
• D. $\theta = \sec^{- 1}\mu$

Answer 1

Answer: (A)

$\theta = \tan^{- 1}\mu$

Answer 2

The various forces acting on the block are as shown in the figure.

From figure

$mg\sin\theta = f$ …… (i)

$mg\cos\theta = N$ ….. (ii)

Divide (i) by (ii) we get

$\tan\theta = \frac{f}{N} = \frac{\mu N}{N}or\theta = \tan^{- 1}(\mu)$