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  4. A moving body of mass m and velocity 3 km / hr. Collides with a body at rest and of mass 2 m and then sticks to it. Now the combined mass starts to move, then the combined velocity will be :

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Q. A moving body of mass $m$ and velocity $3\, km / hr$. Collides with a body at rest and of mass $2\, m$ and then sticks to it. Now the combined mass starts to move, then the combined velocity will be :

AIPMTAIPMT 1996Work, Energy and Power

Solution:

Mass of body $\left(m_{1}\right)=m$;
Velocity of first body $\left(u_{1}\right)=3\, km /$ hour;
Mass of second body in rest $\left(m_{2}\right)=2 m$
and velocity of second body $\left(u_{2}\right)=0$.
After combination, mass of the body $(M)=m+2 m=3 m$
From the law of conservation of momentum, we get
$M v=m_{1} u_{1}+m_{2} u_{2}$
or $3 m v=(m \times 3)+(2 m \times 0)=3 m$
or $v=1\, km /$ hour.