A hollow sphere of mass `'m'` and radius `R` rests on a smooth horizontal surface. A simple pendulum having string of length `R` and bob of mass `m` hangs from top most point of the sphere as shown. A bullet of mass `'m'` and velocity `'v'` partially penetrates the left side of the sphere and stick to it. The velocity of the sphere just after collision with bullet is .

Options

A. `(v)/(2)`
B. `(v)/(3)`
C. `(2v)/(3)`
D. `(3v)/(5)`

Answer

A

Explanation

For the duration of collision the pendulum does not exert any force on the sphere in the horizontal direction.
Hence the horizontal momentum of bullet `+` sphere is conserved for the duration of collision . Let `v'` be the velocity of bullet and sphere just after the collision.
`:.` from conservation of momentum ltbr. `(m+m)v'=mv`
or `v'=(v)/(2)`