Question

A ball P of mass 2 kg undergoes an elastic collision with another ball Q initially kept at rest. After the collision, ball P continues to move in its original direction with a speed one-fourth of its original speed. What is the mass of ball Q?

• A. 0.9 kg
• B. 1.2 kg
• C. 1.5 kg
• D. 1.8 kg

Answer 1

The correct option is B 1.2 kg

Since the collision is elastic, both momentum and kinetic energy are conserved. If m is mass of ball Q and v’ its speed after the collision, the law of conservation of momentum gives
$2v=2\times \frac{v}{4}+m{v}^{{}^{\prime }}$
Where v is the original speed of ball P. thus
$m{v}^{{}^{\prime }}=\frac{3v}{2}or{v}^{{}^{\prime }}=\frac{3v}{2m}$ (i)
The law of conservation of energy gives
$\frac{1}{2}\times 2\times v^2=\frac{1}{2}\times 2\times {\left(\frac{v}{4}\right)}^2+\frac{1}{2}m{v}^{{}^{\prime }2}$
or $m{v}^{{}^{\prime }2}=\frac{15v^2}{8}$ (ii)
Using (i) in (ii) we get m = 1.2 kg. Hence the correct choice is (b).