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A solid sphere of mass M and radius R is...

A solid sphere of mass M and radius R is placed on a smooth horizontal surface. It is given a horizontal impulse J at a height h above the centre of mass and sphere starts rolling then, the value of h and speed of centre of mass are –

A

`h=(2)/(5)R and v=(J)/(M)`

B

`h=(2)/(5)R and v=(2)/(5) (J)/(M)`

C

`h=(7)/(5)R and v=(7)/(5)(J)/(M)`

D

`h=(7)/(5)R and v= (J)/(M)`

Text Solution

Verified by Experts

The correct Answer is:
A
Let the force producing impulse J is F then
`F xx h=(2)/(5) mR^(2)xx alpha`
and F = ma (where `a=R alpha`)
`:.` mah `=(2)/(5) mRa rArr h=(2)/(5)R`
Also impulse = change in momentum
or `J=Mv`
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