A hollow cylinder is rolling down an inclined plane which is inclined at an angle of 30 ∘ to the horizontal. Find its speed after travelling a distance of 10 m .

As the hollow cylinder is sliding down which means its potential energy is getting converted into kinetic energy. So, its total mechanical energy will be conserved. Let m , v , ω , r be the mass, linear speed, angular speed and radius of the cylinder respectively. Now, considering the figure above we have; From triangle A B C ; A C 10 = sin 30 ∘ ⇒ A C = 10 2 = 5 m . Now, Potential energy at point A = Kinetic energy at point B (Rotational kinetic energy + Translational kinetic energy) ⇒ m g × 5 = 1 2 m v 2 + 1 2 I ω 2 ( I = m r 2 is the moment of inertia of the cylinder ) ⇒ 5 m g = 1 2 m v 2 + 1 2 × m r 2 × v 2 r 2 ( as v = r ω ) ⇒ 5 g = v 2 2 + v 2 2 ⇒ v = 5 × 10 = 7 . 1 m s - 1 ( taking value of acceleration due to gravity; g = 10 m s - 2 ) Hence, the required speed of the cylinder is 7 . 1 m s - 1 .

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>BEGINNER'S BOX - 6>Q 4

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A ring, a disc and a solid sphere are simultaneously released to roll down from the top of a rough inclined plane of height $h$ . Write the order in which these three bodies will reach the bottom?

Important Questions on Rotational Mechanics

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>BEGINNER'S BOX - 6>Q 5

A hollow cylinder is rolling down an inclined plane which is inclined at an angle of

30^{\circ}

to the horizontal. Find its speed after travelling a distance of

10 m

.

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>Exercise (Conceptual Questions)>Q 1

Essential characteristic of equilibrium is

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>Exercise (Conceptual Questions)>Q 2

If the equation for the displacement of a particle moving in a circular path is given by,

(θ) = 2 t^{3} + 0.5

, where

θ

is in radians and

t

in seconds, then the angular velocity of the particle after

2 s

from its start is

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>Exercise (Conceptual Questions)>Q 3

Two particles having masses

M

and

m

are moving in a circular path having radius

R

and

r .

If their time periods are same, then ratio of angular velocity will be

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>Exercise (Conceptual Questions)>Q 4

Angular velocity of minute hand of a clock is:

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>Exercise (Conceptual Questions)>Q 5

A frictionless track ABCDE ends in a circular loop of radius $R$ . A body slides down the track from point A which is at a height $h = 5 cm$ . Maximum value of $R$ for the body to successfully complete the loop is :-

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>Exercise (Conceptual Questions)>Q 6

A wheel is rotating about a fixed axis. Find the moment of inertia of the wheel about the axis of rotation, when its angular speed is

30 rad s^{- 1}

and its kinetic energy is

360 J

.

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Beta Question Bank for Medical: Physics>Chapter 10 - Rotational Mechanics>Exercise (Conceptual Questions)>Q 7

Two uniform identical discs roll down on two inclined planes of length s and 2s respectively as shown in the figure. Find the ratio of velocities of the two discs at the points A and B of the inclined planes ?
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