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  4. A body mass of 1 kg, initially at rest explodes and breaks into three parts. The masses of the parts are in the ratio 1: 1: 3 . The two pieces of equal mass fly off perpendicular to each other with a speed of 30 m / s each. The velocity of the heavier part in m / s is

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Q. A body mass of $1 \,kg$, initially at rest explodes and breaks into three parts. The masses of the parts are in the ratio $1: 1: 3 .$ The two pieces of equal mass fly off perpendicular to each other with a speed of $30 \,m / s$ each. The velocity of the heavier part in $m / s$ is

TS EAMCET 2015

Solution:

Initial momentum before explosion is zero. Final momentum after explosion.
image
$\sqrt{2} \frac{m}{4} \times 30-\frac{3 m}{4} v^{\prime}$
From conservation of momentum
Initial momentum = Final momentum
$\Rightarrow \sqrt{2} \frac{m}{4} \times 30-\frac{3 m}{4} v^{\prime}=0$
$\Rightarrow v^{\prime}=10 \sqrt{2} m / s$