Question

A bomb of mass m is moving in x direction with veloc­ity u when it separates into masses $\frac{1}{3}$m and $\frac{2}{3}$m mov­ing horizontally in the same plane. If an additional en­ergy of Amu¹is generated, the relative speed of two masses is

• A. 3u
• B. 4u
• C. 6u
• D. 8u.

Answer 1

Answer: (C)

6u

Answer 2

By conservation of momentum

mu = $\frac{mu_{1}}{3} + \frac{2}{3}mu_{2}$

or 3u = u₁ + 2u₂ ……….. (i)

also additional energy

= $\left( \frac{1}{2}\frac{mu_{1}^{2}}{6} + \frac{12}{2}\frac{2mu_{2}^{2}}{6} \right) - \frac{1}{2}mu^{2}$

or 4mu² = $\frac{mu_{1}^{2}}{6}$ + $\frac{2mu_{2}^{2}}{6}$ - $\frac{1}{2}mu^{2}$

or 24mu² = mu₁² + 2mu₂² – 3mu²

or 27mu² = mu₁² + 2mu₂²

Solving (i) and (ii) u₁ = 5u and u₂ = -u

∴ Relative velocity = 5u - (-u) = 6u