question_answer

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 fragments is \[6.4\times {{10}^{4}}J\]. What is the K.E. of the smaller fragment                                            [DCE 2004]

A)                 \[2.5\times {{10}^{4}}J\]

B)                    \[3.5\times {{10}^{4}}J\]

C)                 \[4.8\times {{10}^{4}}J\]              

D)                 \[5.2\times {{10}^{4}}J\]

Correct Answer: C

Solution :

    As the momentum of both fragments are equal therefore \[\frac{{{E}_{1}}}{{{E}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}=\frac{3}{1}\]i.e. \[{{E}_{1}}=3{{E}_{2}}\]               ?(i)                 According to problem \[{{E}_{1}}+{{E}_{2}}=6.4\times {{10}^{4}}J\]          ?(i)                 By solving equation (i) and (ii) we get                 \[{{E}_{1}}=4.8\times {{10}^{4}}J\]and \[{{E}_{2}}=1.6\times {{10}^{4}}J\]