Question

A hemisphere S and a particle P are of same mass m = 72 kg. P is
dropped from a height 'h'. S is kept on a smooth horizontal surface. The
friction between P and S is also absent. P collides elastically with S at the
point shown in the figure. After collision the velocity of the particle becomes
horizontal. Find ratio of impulse of ground on hemisphere to speed of
hemisphere after collision ?​

Answer 1

Answer:

The particle after starting from point A reaches the point P where it leaves contact with the surface.

For the particle to loose contact at P, cosθ=

3

2

∴ Height from the ground OB=rcosθ=

3

2r

Answer 2

Answer:

Given =  mass (m) = 72Kg

              particle =  p

              height = h

              smooth horizontal = S

to find = ratio of impulse of impulse of ground on hemisphere to speed of hemisphere after collision ?​

solution = particle after starting from point A the point P where it leaves contact with surface.

for particle p,

        cosθ = 3/2

   ∴   h  from ground ,

       OB= rcosθ = 3/2r

so we can conclude that the ratio of  impulse of ground on hemisphere to speed of  hemisphere after collision is 3:2