Home
Class 11
PHYSICS
A hoop and a solid cylinder have the sam...

A hoop and a solid cylinder have the same mass and radius. They both roll,without slipping, on horizontal surface. If their kinetic energies are equal -

A

the hoop has a greater translational speed than the cylinder

B

the cylinder has a greater translational speed than the hoop

C

the hoop and the cylinder have the same translational speed

D

the hoop has a greater rotational speed than the cylinder.

Text Solution

Verified by Experts

The correct Answer is:
B
`KE_(hoop) = KE_(cylinder)`
`[(1)/(2) mv_(cm)^(2) (1 + K^(2) //R^(2))]_("hoop") = [(1)/(2) mv_(cm)^('2)(1 + K^(2) //R^(2))]_("cylinder")`
`(1)/(2) mv_(cm)^(2) (1+1) = (1)/(2) mv_(cm)^('2) (1 +(1)/(2))`
`2 xx (1)/(2) mv_(cm)^(2) = (3)/(2) xx (1)/(2) mv_(cm) rArr v_(cm)^(2) = (4)/(3) v_(cm)^(2)`
`v_(cm) = (2)/(sqrt(3)) v_(cm)`.
Promotional Banner

Similar Questions

Explore conceptually related problems

A solid sphere of mass m and radius R rolls without slipping on a horizontal surface such that v_(c.m.)=v_(0) .

A solid cylinder of mass M and radius R rolls without slipping on a flat horizontal surface. Its moment of inertia about the line of contact is ?

A thin ring and a solid disc of same mass and radius are rolling with the same linear velocity. Then ratio of their kinetic energies is

A circular hoop rolls without slipping on a flat horizontal surface. Which one of the following is necessarily true?

A solid sphere and a solid cylinder having the same mass and radius, rolls down the same incline. The ratio of their acceleration will be

A ring, disc, hollow sphere and solid sphere roll on a horizontal surface with the same linear speed. If they have same mass and radius and move without slipping, rotational kinetic energy is more for

A solid sphere rolls without slipping along a horizontal surface. What percentage of its total kinetic energy is rotational kinetic energy?

A solid sphere of mass 1 kg and radius 10 cm rolls without slipping on a horizontal surface, with a velocity of 20 cm/s. The total kinetic energy of the sphere is

A solid sphere of mass 1 kg and radius 10 cm rolls without slipping on a horizontal surface, with a velocity of 20 cm/s. The total kinetic energy of the sphere is