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A bomb of mass 3 m kg explodes into two ...

A bomb of mass 3 m kg explodes into two pieces of mass m kg and 2 m kg. If the velocity of m kg mass is `16 ms^(-1)`, the total kinetic energy in the explosion is :

A

192 mJ

B

96 mJ

C

384 mJ

D

768 mJ

Text Solution

Verified by Experts

The correct Answer is:
A
According to law of conservation of momentum
Total momentum = `m_(1) v_(1) + m_(2)v_(2)`
`0 = m xx 16 + 2m xx v_(2)`
`v_(2) = - (m xx 16)/(2m) = - 8 m //s`.
Now, Total kinetic energy `= (1)/(2) m_(1)v_(1)^(2) + (1)/(2) m_(2)v_(2)^(2)`
= `(1)/(2) xx m xx (16)^(2) + (1)/(2) xx 2 m xx 8^(2)`
= `(1)/(2) m xx 256 + (1)/(2) xx 2m xx 64`
= `128 m + 64 m`
`= 192 mJ.`
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