A hemispherical bowl of uniform mass distribution of mass ‘M’ is at rest on frictionless horizontal ground sur- face. There is a small insect of mass 'm' on bowl at point ‘A’ of the bowl at rest. Now the insect moves with constant speed ‘v’ relative to bowl in vertical plane. Assume that insect does not slip on the bowl.

When the insect is at point ‘P’ of the hemispherical bowl the acceleration of bowl is :

Options

A. Zero
B. `(m/(M+m))(v^(2))/R cos theta` horizontally towards left
C. `(M/(M+m))(v^(2))/R sin theta` horizontally towards right
D. `(m/(M+m))(v^(2))/R cos theta` horizontally towards right

Explanation

Momentum of system in horizontal will remain conserved, so
`MV=m(vsin theta-V)`
`rArr V=(mv)/(M+m)sin theta`
`(dV)/(dt)=(mv)/(M+m)cos theta((d theta)/(dt))`
`((dV)/(dt))=(m/(M+m))(v^(2))/Rcos theta`