Question

A hollow smooth uniform sphere $A$ of mass m rolls without sliding on a smooth horizontal surface. It collides head on elastically with another stationary smooth solid sphere $B$ of the same mass m and same radius. The ratio of kinetic energy of $B$ to that of $A$ just after the collision is :

• A. $1:1$
• B. $2:3$
• C. $3:2$
• D. $4:3$

Answer 1

The correct option is C $3:2$

when two identical bodies collide & one body is at rest initially then linear momentum is totally transferred to other body.Let the velocity of sphere A initially was V

final velocity of A= 0

final velocity of other sphere B is V

kinetic energy of B =mV²/2 ..............1

kinetic energy of A = IW²/2

=mV²/3 ................2 (Isphere = 2/3 mr² )

eq1 / eq2 =3/2.