Question

A spherical ball of mass $1$ kg moving with a uniform speed of $1$ m/s collides symmetrically with two identical spherical balls of mass $1$ kg each at rest touching each other. If the two balls move with $0.5$ m/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. $0.125$ J
• B. $0.5$ J
• C. $1.0$ J
• D. $0.75$ J

Answer 1

The correct option is A $0.125$ J

Initial momentum (before collision),

$P_1$= 1kg$\times$1 m/s= 1kg m/s

Initial kinetic energy, ${K.E}_1$= $\frac{1}{2}\times 1\times 1$

=0.5 J

After collision, the two stationary balls start moving at an angle of ${60}^o$. and the first ball moving with a velocity (say v)

From conservation of momentum

1= $1\times 0.5cos{60}^o+1\times 0.5Cos{60}^o+1\times v$

1= 0.5+v

v=0.5 m/s

Kinetic energy after collision, ${K.E}_2=\frac{1}{2}\times 1\times {\left(0.5\right)}^2+\frac{1}{2}\times 1\times {\left(0.5\right)}^2+\frac{1}{2}\times 1\times {\left(0.5\right)}^2$

= $\frac{3}{2}\times {\left(0.5\right)}^2$

= 0.375J

Loss in K.E= ${K.E}_1-{K.E}_2$

=(0.5-0.375)J

= 0.125J