First slide

Law of conservation of momentum and it's applications

Question

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

Moderate

A

$2 .5 \times 10^{4} J$
B

$3 .5 \times 10^{4} J$
C

$4 .8 \times 10^{4} J$
D

$5 .2 \times 10^{4} J$

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 $E_{1} + E_{2} = 6 .4 \times 10^{4} J$ …(ii)
By solving equation (i) and (ii) we get
$E_{1} = 4 .8 \times 10^{4} J$ and $E_{2} = 1 .6 \times 10^{4} J$

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