AP EAMCET · PHYSICS · Center of Mass Momentum and Collision
A bomb at rest explodes into three pieces of equal masses. If two pieces move perpendicular to each other, each with a speed \(v\) then the speed of the third piece is
- A V
- B \(\mathrm{v} \sqrt{2}\)
- C \(\frac{\mathrm{v}}{\sqrt{2}}\)
- D \(2 \mathrm{v}\)
Answer & Solution
Correct Answer
(B) \(\mathrm{v} \sqrt{2}\)
Step-by-step Solution
Detailed explanation
Apply the conservation of momentum \(\begin{aligned} & 3 m \times 0=m \vec{v}_1+m \vec{v}_2+m \vec{v}_3 \\ & 0=m v \hat{i}+m v \hat{j}+m \vec{v}_3 \\ & \vec{v}_3=-v \hat{i}-v \hat{j} \\ & \left|v_3\right|=\sqrt{(-v)^2+(-v)^2}=\sqrt{2} v \end{aligned}\)
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