Question

A goalkeeper in a game of football pulls his hands backward after holding the ball shot at the goal. This enables the goalkeeper to

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Solution

The correct option is **D**

Decrease the rate of change in momentum

**The explanation for the correct option**

**Option **$B$and **Option **$D$

- After holding the ball, the goalkeeper pulls his hands backward to slow down the rate of change of momentum while increasing the time.
- The force is directly related to the rate of change of momentum, this allows less force to be exerted on his hands if he moves his hands backward.
- According to newton's second law, the rate of change of momentum of a body is equal to the force applied to the body.

**From newton's second law **

Rate of change of momentum$=\frac{d\left(mv-mu\right)}{dt}$

$m=Massofthebody\phantom{\rule{0ex}{0ex}}u=Initialvelocityofthebody\phantom{\rule{0ex}{0ex}}v=Finalvelocityofthebody$

$=m\xb7\frac{d\left(v-u\right)}{dt}\phantom{\rule{0ex}{0ex}}=m\xb7a\left[\because Acceleration\left(a\right)=\frac{d\left(v-u\right)}{dt}\right]\phantom{\rule{0ex}{0ex}}=force$

From the above derivation, we can see that if we increase the time of ball travel the rate of change in momentum of the ball decreases which results in a decrease in the force of the ball.

**Hence, the correct options are **$B$ **and** $D$.

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