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NEETPhysicsCenter of Mass, Momentum and Collision

Two bodies, A and B, are moving with uniform velocities. The ratio of their masses is 1 : 4 and the ratio of their linear momenta is 2 : 1 . The ratio of the distances covered by them in the same time interval is:

Options

  1. A1 : 2
  2. B1 : 8
  3. C2 : 1
  4. D8 : 1

Correct answer

D. 8 : 1

Step-by-step solution

Let the masses of bodies A and B be m_ A and m_ B , and their linear momenta be p_ A and p_ B . Given: m_ A m_ B = 1 4 p_ A p_ B = 2 1 The velocity of a body is given by v = p m . The distance covered in time t is d = v t = p m t . Since the time interval t is the same for both bodies, the ratio of distances covered is: d_ A d_ B = p_ A / m_ A p_ B / m_ B = ( p_ A p_ B ) ( m_ B m_ A ) Substituting the given values: d_ A d_ B = ( 2 1 ) ( 4 1 ) = 8 1 Hence, the ratio of the distances covered is 8 : 1 . Answer: 8 : 1

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