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## Homework Statement

A thin spherical shell lying on a rough horizontal floor is hit by a cue in such a way that the line of action of force passes through the centre of the shell.as a result the shell starts moving with a linear speed v without any initial angular velocity.find the linear speed of the shell after it starts purely rolling.

## Homework Equations

1/2mv

^{2}=1/2mv'

^{2}+1/2Iω

^{2}

## The Attempt at a Solution

i would use the principle of conservation of energy here as angular momentum is not conserved here because there is an external torque acting on it by friction.

1/2mv

^{2}=1/2mv'

^{2}+1/2Iω

^{2}(v' is the linear velocity of the cue after it starts purely rolling)

v

^{2}=(3/2)v'

^{2}(I=1/2mr2

^{2})

But the answer happens to be v'=3v/5