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A bomb at rest splits into three identical parts

Question :- A bomb at rest splits into three identical parts. If two pieces are moving at right angles to each other with same velocity v m/s, the velocity of third fragment is

(A) v/√2

(B) v/2

(D) v√2

Solution :-

Before splitting, initial linear momentum, p_i = 0.

Let the three identical masses are m/3 each.

After splitting, final linear momentum, $\displaystyle {{\overrightarrow{p}}_{f}}=\frac{m}{3}(v\widehat{i})+\frac{m}{3}(v\widehat{j})+\frac{m}{3}(\overrightarrow{v'})$