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Question
Two balls A and B of masses m and 2 m are in motion with velocities 2v and v, respectively. Compare:
(i) Their inertia.
(ii) Their momentum.
(iii) The force needed to stop them in the same time.
Solution
(i) Inertia of body A:Inertia of body B :: m:2m
Or, Inertia of body A:Inertia of body B :: 1:2.
(ii) Momentum of body A = m (2v) = 2mv
Momentum of body B = (2m) v = 2mv
Momentum of body A:Momentum of body B :: 2 mv:2mv
Or, Momentum of body A:Momentum of body B :: 1:1.
(iii) According to Newton's 2nd law of motion, rate of change of momentum is directly proportional to the force applied on it. Therefore,
Force needed to stop A:Force needed to stop B :: 1:1.
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