Two balls A and B of masses m and 2m are in motion with velocities 2v and v respectively. Compare (i) their inertia, (ii) their momentum, and (iii) the force needed to stop them in same time.
(i) Comparing inertia of two bodies A and B;
The inertia of body A: Inertia of body B :: m:2m or 1:2
(ii) Comparing the momentum of both bodies
Momentum of body A = m(2v) = 2mv
Momentum of body B = (2m)v= 2mv
The momentum of body A: Momentum of body B :: 2mv:2mv or 1:1
(iii) Comparing the force needed to stop both the bodies at the same time
Rate of momentum change is directly proportional to the force applied on a body as per
Newton’s second law of motion. Hence;
The force required to stop A: Force required to stop B:: 1:1
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