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A bullet of mass m is fired horizontally...

A bullet of mass m is fired horizontally into a large sphere of mass M and radius R resting on a smooth horizontal table.

The bullet hits the sphere at a height h from the table and sticks to its surface. If the sphere starts rolling without slippng immediately on impact, then

A

`(h)/(R ) = (4m + 3M)/( 2(m + M))`

B

`(h)/(R ) = (m + 3M)/( m + 2M)`

C

`(h)/( R ) = (10 m + 7M)/( 5(m + M))`

D

`(h)/(R ) = (4m + 3M)/( m + M)`

Text Solution

Verified by Experts

The correct Answer is:
C
Apply conservation of linear momentum
`mv = ( m + M)v_0`
` mv sin theta R = ((2)/(5) MR^(2) + mR^(2)) omega_0`
`mv ( (h-R)/(R ))R = ((2M + 5M))/( 5) omega_(0) R^(2)`
`(m + M) (h-R) omega_(0) R = ((2M + 5M))/(5) omega_(0) R^(2)`
` (h)/(R) = ((10 m + 7M))/(5 ( m + M))`
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