Question

# A bomb of mass 4 m at rest, explodes into three pieces of masses in the ratio 1:1:2. The two identical pieces fly in mutually perpendicular directions, each with a velocity v. The third piece is making an angle α with the line of motion of each piece. Find α.

A
450
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B
900
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C
1350
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D
1800
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Solution

## The correct option is B 1350Let the two identical pieces fly along ^i and ^j directions,Using momentum conservationInitial momentum =0, therefore,mv^i+mv^j+2m→x=0→x=−v2(^i+^j)Let α be the angle between →x and ^i.By taking dot product of →x and ^i, we get,→x.^i=|→x||^i|cosα⇒−v2=√(v2)2+(v2)2cosα⇒−v2=v√2cosα⇒cosα=−1√2⇒α=1350

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