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Q.

A body of mass 1 kg initially at rest, explodes and breaks into three fragments of masses in the ratio 1 : 1: 3. The two pieces of equal mass fly off perpendicular to each other with a speed of 15 ms-1 each. What is the velocity of the heavier fragment?

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a

102ms−1

b

53ms−1

c

103ms−1

d

52ms−1

answer is D.

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Detailed Solution

Conservation of momentum during explosion yields⇒ P→1+P→2+P→3=0⇒P3→=P→1+P→2⇒ m3 v3→=m1v→1+m2v→2 since v→1⊥v→2⇒ v3→=m1m32v12+m2m32v22⇒ 132(15)2+132(15)2 ∴m1:m2:m3=1:1:3⇒ v3=52ms−1
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