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

Options

A. `2.5xx10^(4)J`
B. `3.5xx10^(4)J`
C. `4.8xx10^(4)J`
D. `5.2xx10^(4)J`

Answer

C

Explanation

As the momentum of both fragments are equal therefore
`(E_(1))/(E_(2))=(m_(2))/(m_(1))=(3)/(1)` i.e. `E_(1)=3 E_(2) " "` …(i)
According to problem `E_(1)+E_(2)=6.4xx10^(4)J " "` …(ii)
By solving equation (i) and (ii) we get
`E_(1)=4.8xx10^(4)J` and `E_(2)=1.6xx10^(4)J`