Question

A solid ball of mass M = 2.0 kg and radius R = 0.25 m starts from rest at a height h = 3.0 m above the bottom of the path. It rolls without slipping down the left side of the path. The right side of the path is frictionless. Moment of inertia of a hollow sphere is � = ! ! ��!. v What is the linear speed

Answer 1

6.48 m/s

Step-by-step explanation:

We are given that

Mass,M=2 kg

Radius,R=0.25 m

Height,h=3 m

Moment of inertia of solid sphere=
`I=(2)/(5)MR^2`

We have to find the linear speed.

`\omega=(v)/(R)`

By law of conservation of energy

`mgh=(1)/(2)I\omega^2+(1)/(2)mv^2`

`mgh=(1)/(2)I((v)/(R))^2+(1)/(2)mv^2=(1)/(2)v^2((I)/(R^2)+m)`

Where
`g=9.8m/s^2`

Substitute the values

`2* 9.8* 3=(1)/(2)((2)/(5R^2)MR^2+M)=(7)/(10)Mv^2=(7)/(10)(2)v^2`

`v^2=(2* 9.8* 3* 10)/(7* 2)`

`v=\sqrt{(2* 9.8* 3* 5)/(7)}`

`v=6.48m/s`