Question

The object at rest suddenly explodes into three parts with the mass ratio 2:1:1. The parts of equal masses move at right angles to each other with equal speeds. The speed of the third part after the explosion will be

• A. 2v
• B. v/ $\sqrt{2}$
• C. v/2
• D. $\sqrt{2}$ v

Answer 1

Answer: (B)

v/ $\sqrt{2}$

Answer 2

Let the speed of the third part be ${{v}_{3}}.$ Applying the law of conservation of momentum, we have $\sqrt{p_{1}^{2}+p_{2}^{2}}=p$ $\Rightarrow$ $p_{1}^{2}+p_{2}^{2}={{p}^{2}}$ $\therefore$ ${{({{m}_{1}}{{v}_{1}})}^{2}}+{{({{m}_{2}}{{v}_{2}})}^{2}}={{({{m}_{3}}{{v}_{3}})}^{2}}$ $\Rightarrow$ ${{(m\times v)}^{2}}+{{(m\times v)}^{2}}={{(2m\times {{v}_{3}})}^{2}}$ $\Rightarrow$ ${{m}^{2}}{{v}^{2}}+{{m}^{2}}{{v}^{2}}=4{{m}^{2}}v_{3}^{2}$ $\Rightarrow$ $2{{m}^{2}}{{v}^{2}}=4{{m}^{2}}v_{m}^{2}$ $\Rightarrow$ ${{v}_{3}}=\frac{v}{\sqrt{2}}$