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

Options

A. `(h)/(R )=(4m+3M)/(2(m+M))`
B. `(h)/(R )=(m+3M)/(m+2M)`
C. `(h)/(R )=(10m+7M)/(5(m+M))`
D. `(h)/(R )=(4m+3M)/(m+M)`

Answer

C

Explanation

Apply conservation of angular momentum
`mv sinthetaR=((2)/(5)MR^(2)+mR^(2))omega_(0)`
`mv((h-R)/(R))R=((2M+5m))/(5)omega_(0)R^(2)implies(m+M)(h-R)omega_(0)` ,br> `R=((2M+5m))/(5)omega_(0)R^(2)implies(h)/(R )=((10+7m))/(5(m+M))`