Question

A uniform rod of length L Lies on a smooth horizontal table . A particle moving on the table strikes the rod perpendicularly at an end and stops . find the distance travelled by the centre of the rod by the rod by the time it turns through a right angle . Show that if the mass of the rod is four times that of particle , the collision is elastic . ​

Answer 1

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Let the mass of the particle = m &

The mass of the rod = M

Let the particle strikes the rod with a velocity V.

If we take the two body to be a system,

Therefore the net external torque & net external force = 0

Therefore Applying laws of conservation of linear momentum

MV' = mV (V' = velocity of the rod after striking)

V' / V = m / M Again applying laws of conservation of angular momentum

$=>\frac{mVR}{2} = l\pi$

$=> \frac{mVR}{2} = \frac{MR^{2} }{12} X \frac{\pi }{2t} => t = \frac{MR\pi }{M12XV}$

$Therefore\:Distance\:travelled:-$

$V't = V'(\frac{MR\pi  }{m12\pi } )= \frac{m}{M} X \frac{M}{m}  X\frac{R\pi }{12} =\frac{R\pi }{12}$

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