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A bomb of mass 30 kg at rest explodes i...

A bomb of mass `30 kg` at rest explodes into two pieces of mass `18 kg` and `12 kg`. The velocity of mass `18 kg is 6 m//s`. The kinetic energy of the other mass is

A

524J

B

486J

C

324J

D

256J

Text Solution

Verified by Experts

The correct Answer is:
B

The two parts move at right angles.
`therefore ` Their resultant momentum `=P=sqrt(P_(1)^(2) +P_(2)^(2))`
But `P_(1)=m_(1)v_(1) = 1xx 2 =12 ` kg m/s
`P_(2)=m_(2)v_(2) = 2 xx 8 =16 ` kg m/s
`therefore P = sqrt(12^(2)+16^(2)) = sqrt(144 + 256)`
`=sqrt(400) = 20 `kg m/s
The third part of mass `m_3` has the same momentum . If `v_3` be its velocity `P=m_3 v_3`
`therefore 20 =m_3 xx 4` therefore `m_3 =5 kg`
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