Question

A body of mass m at rest gets exploded into $3$ parts, having masses in the ratio $1:1:3$. Its two parts having equal masses move at right angles to each other with $15m/s^{-1}$ each. The velocity of third is :

• A. $5\sqrt{2}m{s}^{-1}$
• B. $5m{s}^{-1}$
• C. $10\sqrt{2}m{s}^{-1}$
• D. $\sqrt{2}m{s}^{-1}$

Answer 1

The correct option is C $10\sqrt{2}m{s}^{-1}$

Let the mass of each part be $\frac{m}{5},\frac{m}{5},\frac{3m}{5}$

Momentum of each part flying at right angle will be same and at ${45}^0$ with the third part.

$\frac{m}{5}\times 15cos{45}^0+\frac{m}{5}\times 15cos{45}^0=\frac{3m}{5}v$

$\frac{15}{\sqrt{2}}+\frac{15}{\sqrt{2}}=3v$

$v=\frac{10}{\sqrt{2}}$