Question

A spherical ball of mass $1kg$ moving with a uniform speed of $1m/s$ collides symmetrically with two identical spherical balls of mass $1kg$ each at rest touching each other. If the two balls move with $0.5m/s$ in two directions at the same angle of ${60}^o$ with the direction of the first ball, the loss of kinetic energy on account of the collision is:

• A. $0.125J$
• B. $0.5J$
• C. $1.0J$
• D. $0.75J$

Answer 1

The correct option is A $0.125J$

As per conservation of linear momentum in the direction of motion of first ball,

1×1=1×0.5cos60+1×0.5cos60+1×V which gives V=0. 5

So final velocity of the first ball = 0.5 m/s

Loss of kinetic energy =Initial kinetic energy - Final kinetic energy

=$\frac{1}{2}\times 1\times 1^2$ - $\frac{1}{2}\times 1\times {0.5}^2$ - $\frac{1}{2}\times 1\times {0.5}^2$-$\frac{1}{2}\times 1\times {0.5}^2$

=0.5-0.375=0.125J