Question

A mass $3m$, initially at rest at the origin explodes into three fragments of equal mass. Two of the fragments have speed $\nu$ each and move perpendicular to each other. The third fragment will move with a speed

• A. $\frac{\nu}{\sqrt{2}}$
• B. $\frac{\nu}{2}$
• C. $\nu$
• D. $\nu \sqrt{2}$

Hint:

In an explosion, the vector sum of momenta of all fragments must be zero.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
By conservation of momentum, initial momentum = 0.
Step 2: Detailed Explanation:
Let the two fragments move along x and y axes with speed $v$. Their momenta are $mv$ along x and $mv$ along y. The third fragment of mass $m$ must have momentum equal and opposite to the resultant of these two. Resultant momentum = $\sqrt{(mv)^2 + (mv)^2} = mv\sqrt{2}$. So, $mv_3 = mv\sqrt{2} \Rightarrow v_3 = v\sqrt{2}$.
Step 3: Final Answer:
The third fragment moves with speed $\nu \sqrt{2}$.