A cricket ball of mass 150 g collides straight with a bat...

A cricket ball of mass 150 g collides straight with a bat with a velocity of $10 \mathrm{~ms}^{-1}$. Batsman hits it straight back with a velocity of $20 \mathrm{~ms}^{-1}$, If ball remains in contact with bat for $0.18$, then average force exerted by the bat on the ball is (a) $15 \mathrm{~N}$ (b) $45 \mathrm{~N}$ (c) $150 \mathrm{~N}$ (d) $4.5 \mathrm{~N}$

A cricket ball of mass 150 g collides straight with a bat with a velocity of $10 \mathrm{~ms}^{-1}$. Batsman hits it straight back with a velocity of $20 \mathrm{~ms}^{-1}$, If ball remains in contact with bat for $0.18$, then average force exerted by the bat on the ball is
(a) $15 \mathrm{~N}$
(b) $45 \mathrm{~N}$
(c) $150 \mathrm{~N}$
(d) $4.5 \mathrm{~N}$

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Key Concepts

Average Force Calculation

The average force exerted during a collision can be determined by dividing the impulse (or change in momentum) by the time interval over which the collision occurs. This approach allows one to estimate the magnitude of the force even when the force varies during the collision, by providing a single value that would produce the same net effect in changing the object's momentum.

Impulse?Momentum Theorem

The impulse?momentum theorem states that the impulse—defined as the force applied over a certain period of time—is equal to the change in momentum of an object. This theorem provides a direct link between the force exerted during a collision and the resulting change in the speed or direction of the object. It is a fundamental principle in mechanics, especially when analyzing collisions where forces act over short time intervals.

Momentum Change

Momentum is the product of an object's mass and its velocity. In collision problems, it is crucial to calculate the change in momentum by considering the difference between the final and initial momentum vectors. Properly accounting for the directions (signs) of the velocities is essential, as the reversal of direction typically leads to a larger net change in momentum.

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