Home
Class 12
PHYSICS
A sphere of mass m and radius r rolls on...

A sphere of mass m and radius r rolls on a horizontal plane without slipping with the speed u. Now, if it rolls up vertically, the maximum height it would attain will be

A

A)`(3u^(2))/(4g)`

B

B)`(5u^(2))/(2g)`

C

C)`(7u^(2))/(10g)`

D

D)`(u^(2))/(2g)`

Text Solution

Verified by Experts

The correct Answer is:
C
The rolling sphere has rotational as well as translational kinetic energy.
`therefore` Kinetic energy `=(1)/(2)m u^(2)+(1)/(2)Iomega^(2)`
`=(1)/(2)m u^(2)+(1)/(2)((2)/(5)mr^(2))omega^(2)`
`=(1)/(2)m u^(2)+(1)/(5)m u^(2)`
`=(7)/(10)m u^(2) (therefore u=romega)`
From conservation of energy,
potential energy = kinetic energy
i.e., `mgh=(7)/(10)m u^(2)`
or `h=(7u^(2))/(10g)`
Promotional Banner

Similar Questions

Explore conceptually related problems

A solid sphere of mass 3kg rolls on a horizontal surface with a linear speed of 30m/s . Find the total kinetic energy of the sphere.

A solid sphere of mass m and radius R starts from rest and rolls down along an inclined plane of height h without slipping. Calculate the kinetic energy of the sphere when it reaches the ground.

A solid sphere of mass m and radius R starts from rest and rolls down along an inclined plane of height h without slipping. Find the velocity when it reaches the base.