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  4. A lump of clay of mass 10 g travelling with a velocity of 10 cms-1 towards east collides head on with another lump of clay of mass 10 g travelling with velocity of 20 cms-1 towards west. If the two lumps coalesce after collision, what is its velocity, if no external force acts on the system?

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Q. A lump of clay of mass $ 10\,g $ travelling with a velocity of $ 10\,cms^{-1}$ towards east collides head on with another lump of clay of mass $10\,g $ travelling with velocity of $ 20\,cms^{-1}$ towards west. If the two lumps coalesce after collision, what is its velocity, if no external force acts on the system?

Punjab PMETPunjab PMET 2009Work, Energy and Power

Solution:

Let velocity towards east be positive, then velocity towards west is negative.
If $v$ is the velocity of two lumps which are coalesced after collision, then from law of conservation of linear momentum
$m_{1} v_{1}+ m_{2} v_{2} =\left(m_{1}+m_{2}\right) v$
$10 \times 20-10 \times 10 =20 \times v$
$v =\frac{100}{20}=5\, cms ^{-1}$
Hence, $5\, cms ^{-1}$ towards west.