Question

A solid sphere with mass, M, and radius, R, rolls along a level surface without slipping with a linear speed, v. What is the ratio of rotational to linear kinetic energy

Answer 1

`(KE_R)/(KE_L)=(2)/(5)`

Step-by-step explanation:

given,

mass of solid sphere = M

radius = R

linear speed = v

now,

Linear Kinetic energy

`KE_L = (1)/(2)mv^2`...............(1)

Rotational kinetic energy

`KE_R= (1)/(2)I\omega^2`

moment of inertia of the solid sphere

`I = (2)/(5)MR^2`

and v = R ω

`KE_R= (1)/(2)((2)/(5)MR^2)((v)/(R))^2`

`KE_R =(1)/(5)MV^2`............(2)

ration of rotational and Kinetic energy

`(KE_R)/(KE_L)=((1)/(5)MV^2)/((1)/(2)MV^2)`

`(KE_R)/(KE_L)=(2)/(5)`

hence, ratio of rotational to linear kinetic energy is equal to 2/5.