The upper half of an inclined plane of inclination θ is perfectly… | NEET 2013

Q28NEET 2013Medium

Friction on an Incline

The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom, if the coefficient of friction between the block and lower half of the plane is given by

Show answer and solution

Answer: (a)

Let length be $L$ . Work-energy from rest to rest: work by gravity = work against friction.
Gravity over full length: $mg\sin\theta \cdot L$ ; friction only on lower half: $\mu mg\cos\theta \cdot \dfrac{L}{2}$ .
$mgL\sin\theta = \mu mg\cos\theta\,\dfrac{L}{2} \Rightarrow \mu = 2\tan\theta$
So the answer is (a) $\mu = 2\tan\theta$ .

Report a mistake

More questions on Friction on an Incline

A body starts from rest on a long inclined plane of slope 45°. The coefficient of…JEE Main 2013 (22 Apr, Shift 1)
A smooth block is released at rest on a 45° incline and then slides a distance 'd'. The…JEE Main 2005 (AIEEE)
A block rests on a rough inclined plane making an angle of 30° with the horizontal. The…JEE Main 2004 (AIEEE)
A block has been placed on a inclined plane with the slope angle θ, block slides down the…NEET 1993 (AIPMT)
Starting from rest, a body slides down a 45° inclined plane in twice the time it takes to…NEET 1988 (AIPMT)
A block is sliding down on an inclined plane of slope θ and at an instant t = 0 this…JEE Main 2026 (23 Jan, Shift 2)
A block of mass 5 kg is moving on an inclined plane which makes an angle of 30° with the…JEE Main 2026 (28 Jan, Shift 1)
The time taken by a block of mass m to slide down from the highest point to the lowest…JEE Main 2026 (4 Apr, Shift 1)

Friction on an Incline question from NEET 2013

More questions on Friction on an Incline