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A bomb is kept stationary at a point. It...

A bomb is kept stationary at a point. It suddenly explodes into two fragments of masses 1 g and 3 g. the total K.E. of the gragments is `6.4xx10^(4)J`. What is the K.E. of the smaller fragment

A

`2.5xx10^(4) J`

B

`3.5xx10^(4) J`

C

`4.8xx10^(4 )J`

D

`5.2xx10^(4)` J

Text Solution

Verified by Experts

The correct Answer is:
D
`m_1v_1=m_2v_2implies v_1/v_2=m_2/m_1=3/1`
`implies v_1=3v_2`
KE `=1/2 m_1v_1^2 +1/2 m_2v_2^2=6.4 xx10^4`
`implies 1/2 m_(1)v_1^(2) +1/2 (3m_1) (v_1/3)^2 =6.4 xx10^4`
`implies 1/2 m_(1)v_1^(2) +1/3 [1/2 m_1v_1^2] = 6.4 xx10^4`
`implies 1/2 m_(1)v_1^(2) =(6.4 xx10^4 xx3)/(4) = 4.8 xx10^4J`
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