A hollow hemispherical bowl of mass `m` radius `R` is placed on a smooth horizontal surface. A particle (also of mass `m`) strikes the hemi spherical bowl at point `P` and sticks to it. the velocity of particle just after the collision in vertically upwards direction is `(ku)/25`, where `k` is an integer. Find `k`.

Answer

3

Explanation

`V_(y)=omega x costheta=(omegaR)/2`
Using conservation of angular momentum about centre of mass.
`"mu" R/4={2/3mR^(2)-(mR^(2))/4+(5mR^(2))/16}omega+(5mR^(2))/16 omega`
`=25/24mR^(2)omega`
`impliesomega=(6u)/(25R)`
`impliesV_(y)=(3u)/25`