Question

When a cricketer catches a ball in 30 s, the force required is 2.5 N. The force required to catch that ball in 50 s is:

• A. 1.5 N
• B. 1 N
• C. 2.5 N
• D. 3 N
• E. 5 N

Hint:

The force required to stop an object is inversely proportional to the time taken to stop. If the time increases, the force required decreases, assuming the change in momentum remains constant.

Answer 1

The Correct Option is A

The force required to catch the ball depends on the rate of change of momentum. The momentum of the ball is \( p = mv \), and the force required is related to the rate of change of momentum, i.e., \[ F = \frac{\Delta p}{\Delta t} = \frac{mv}{t}. \] Here, \( \Delta p \) is the change in momentum and \( \Delta t \) is the time taken to stop the ball.
The relationship between force and time taken to stop the ball is inversely proportional, meaning that if the time increases, the force required decreases, as long as the momentum change remains the same.
Let \( F_1 = 2.5 \, {N} \) be the force required to stop the ball in \( t_1 = 30 \, {s} \), and \( F_2 \) be the force required to stop the ball in \( t_2 = 50 \, {s} \).
Using the inverse proportionality: \[ \frac{F_1}{F_2} = \frac{t_2}{t_1}. \] Substituting the given values: \[ \frac{2.5}{F_2} = \frac{50}{30} \quad \Rightarrow \quad F_2 = \frac{2.5 \times 30}{50} = 1.5 \, {N}. \]
Thus, the correct answer is option (A), 1.5 N.