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A body of mass (4m) is laying in xy-plan...

A body of mass (4m) is laying in xy-plane at rest. It suddenly explodes into three pieces. Two pieces each mass (m) move perpedicular to each other with equal speeds (v). Total kinetic energy generated due to explosion is

A

` 2mv^2`

B

`4mv^2`

C

`mv^2`

D

`3/2 mv^2`

Text Solution

Verified by Experts

The correct Answer is:
D
`mv(hati) +mv(hatj)=2mv_s`
`implies v_3 = sqrt((v^2+v^2)/(2))=(sqrt2v)/2=v/sqrt2`
`KE=1/2 mv^2 +1/2 mv^2 +1/2 xx 2m xx (v/sqrt2)^2`
`=mv^2 +(mv^2)/2=3/2 mv^2`
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