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A body of mass 4m is lying in xy-plane ...

A body of mass 4m is lying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces, each of mass m move perpendicular to each other with equal speeds v. The total kinetic energy generated due to explosion is

A

`mv^2`

B

`3/2 mv^2`

C

`2mv^2`

D

`4mv^2`

Text Solution

Verified by Experts

The correct Answer is:
B
By conservation of linear momentum ,
`2mv_1=sqrt(2)mv`
`or, v_1=v/(sqrt(2))`
Total KE generated
`=1/2 mv^2+1/2mv^2+1/2(2m)v_1^2`
`=mv^2+mv_1^2=mv^2+1/2mv^2=3/2mv^2`
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