A solid sphere of mass `m` and radius `R` is placed on a smooth horizontal surface. A sudden blow is given horizontally to the sphere at a height `h = 4R//5` above the centre line. If `I` is the impulse of the blow then find
(a) the minimum time after which the highest point `B` will touch the ground.
(b) the displacement of the centre of mass during this internal.

Answer

(a) `t = (pi Rm)/(21)` ;
(b) `s = (pi R)/(2)`.

Explanation

(a) Angular impulse

`I xx (4R)/(5) = I' omega rArr I xx (4R)/(5) = ((2)/(5) mR^(2)) omega`
`omega = (2I)/(mR)` Also `omega = (theta)/(t)`
`t = (theta)/(omega) rArr t = (pi)/(2I//mR) rArr t = (pi Rm)/(2 I)`
(b) Linear impulse
`I = mv, v = (I)/(m)` &
`d = v xx t = (I)/(m) xx (pi Rm)/(2 I) rArr d = (pi R)/(2)`.