A light rope passes over a light frictionless pulley attached to the ceiling. An object with a large mass is tied to one end and an object with a smaller mass is tied to the other end. Both masses are released from rest. Which of the following statement(s) is/are false for the system consisting of the two moving masses while string remains taut?

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the net external force is zero

the velocity of the center of mass is a constant

the center of mass remains at rest

the acceleration of the center of mass is g downward

answer is A, B, C, D.

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Detailed Solution

If larger mass comes down with acceleration $a,$ $a_{cm} = \frac{aM - am}{M + m} = a (\frac{M - m}{M + m})$

$∴$ COM is not at rest and net force on the system $= (M + m) \frac{(M - m)}{(M + m)} a = (M - m) a$

Velocity of COM changes continuously.

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