91Ó°ÊÓ

The impulse of a golf ball and a bean bag can be obtained when a force is exerted by the ground in a small interval of time. There is a change in the momentum of the bean bag and a golf ball can be observed.

Then, determine the impulse for each case.

It is given that the bean bag stays at the rest position after hitting the ground. The mass of the golf ball and the bean bag is the same.

The momentum of the bean bag is equal to an upward impulse force exerted by the ground.

An impulse of the system is equal to the change in the momentum of the system. The impulse can be calculated as

\(I = m\left( {{v_f} - {v_i}} \right)\).

Here,\({v_f}\)is the final velocity of the bean bag is equal to zero,\({v_i}\)is the initial velocity of the bean bag, and m is the mass of the bean bag.

Substitute the values in the above equation.

\(\begin{aligned}{c}I = m\left( {0 - {v_i}} \right)\\ = - m{v_i}\end{aligned}\)

Here, the negative sign indicates the opposite direction of velocity.

The magnitude of the impulse is equal to the value of the initial momentum.

It is given that the golf ball rebounds back in the upward direction, having the same value of momentum. But during the rebound, the momentum acts in an upward direction, which is opposite to the initial momentum during the hitting with the ground.

An impulse of the system is equal to the change in the momentum of the system. The impulse can be calculated as

\({I_2} = m\left( {{v_{{f_2}}} - {v_{{i_2}}}} \right)\).

Here,\({v_{{f_2}}}\)is the final velocity of the golf ball is equal to\(\left( { - {v_{{i_2}}}} \right)\),\({v_{{i_2}}}\)is the initial velocity of the golf ball, and m is the mass of the golf ball.

Substitute the values in the above equation.

\(\begin{aligned}{c}{I_2} = m\left( { - {v_{{i_2}}} - {v_{{i_2}}}} \right)\\ = - 2m{v_{{i_2}}}\end{aligned}\)

Here, the negative sign indicates the opposite direction of velocity.

An impulse force is exerted by the ground in the upward direction, which is equal to two times the momentum of the golf ball.

The momentum of the golf ball is equal to twice the value of the initial momentum. So, in the case of the golf ball, the magnitude of impulse increases.

Option (a) can be the correct option because the momentum of the golf ball increases and thus increases the values of impulse.

Option (b) is incorrect because the bean bag impulse is less in magnitude than the golf ball.

Option (c) is incorrect because the magnitude of an impulse is not the same in both cases.

Option (d) is incorrect because complete information is given, and from the above analysis, it can be concluded which of them will experience more impulse.

Hence, from the above analysis of options, the golf ball experiences greater impulse from the ground.

Thus, option (a) is correct.