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Physics · LAWS OF MOTION
हिन्दीA batsman hits back a ball of mass \( m \) moving with speed \( v \) straight in the direction of the bowler without changing its speed. The contact time between the bat and the ball is \( \Delta t \). In a second situation, the mass of the ball is doubled, its speed is increased by 50%, and the duration of contact is reduced to half. What is the ratio of the average force exerted on the ball in the second situation to that in the first situation?
Correct answer · Option 3
6 : 1
Explanation
Change in momentum in 1st case: \( \Delta p_1 = 2mv \), average force \( F_1 = \frac{2mv}{\Delta t} \). In 2nd case: \( m' = 2m \), \( v' = 1.5v \), \( \Delta t' = 0.5 \Delta t \). Change in momentum \( \Delta p_2 = 2(2m)(1.5v) = 6mv \), average force \( F_2 = \frac{6mv}{0.5\Delta t} = 12\frac{mv}{\Delta t} = 6 F_1 \). Ratio \( F_2 : F_1 = 6 : 1 \).
