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JIPMER 2017
Exam
JIPMER
Year
2017
Subject
Physics
Chapter
Center of Mass, Momentum and Collision

JIPMER 2017 · Physics · Center of Mass, Momentum and Collision

A stick of length L and mass M lies on a frictionless horizontal...

A stick of length LL and mass MM lies on a frictionless horizontal surface on which it is free to move in any way. A ball of mass mm moving with speed VV collides elastically with the stick as shown in fig below. If after the collision, the ball comes to rest, then what should be the mass of the ball? A stick of length L and mass M lies on a frictionless horizontal surface on which it is free to move in any way. A ball

Options

  1. Am=2Mm=2 M
  2. Bm=M
  3. Cm=M/2m=M / 2
  4. Dm=M/4m=M / 4

Correct answer

D. m=M/4m=M / 4

Step-by-step solution

Applying the law of conservation of momentum mV=MV...(i)m V=M V...(i) By conservation of angular momentum mV(L/2)=(ML212)ω...(ii)m V(L / 2)=\left(\frac{M L^2}{12}\right) \omega...(ii) As the collision is elastic, we have 12mV2=12MV2+12Iw2...(iii)\frac{1}{2} m V^2=\frac{1}{2} M V^2+\frac{1}{2} I w^2...(iii) Substituting the values, we get m=M/4m=M / 4
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