Question

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.

March 13, 2024

Answer

(i) Mass of A = m

Mass of B = 2m

Inertia of A : Inertia of B = m : 2m

= 1 : 2

Hence, ratio of their inertia = 1 : 2

(ii) Momentum = mass × velocity

p_A : p_B = m_Av_A : m_Bv_B

= m × 2v : 2m × v

= 2mv : 2mv = 1 : 1

Hence, ratio between the momentum of A and B is 1 : 1

(iii) According to Newton’s second law of motion, the rate of change of momentum of a body is directly proportional to the force applied on it and as the ratio of momentum between A and B is 1 : 1, hence, ratio of force needed to stop A and B is also 1 : 1

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