In two different experiments, an object of mass 5 ~kg moving with a speed of 25 ~ms^-1 hits two different walls and comes to rest within (i) 3 second, (ii) 5 seconds, respectively. Choose the correct option out of the following :

Impulse will be same for both the cases but the average force will be different.

Impulse and average force acting on the object will be same for both the cases.

Average force will be same for both the cases but the impulse will be different.

Average force and impulse will be different for both the cases.

Center of Mass PYQ — JEE Main 2022 · 28 Jul · Shift 1 · Q49 with Solution

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Correct answer: B

Mass of object: $m = 5\,\text{kg}$
Initial speed: $u = 25\,\text{m s}^{-1}$
Final speed: $v = 0$
Two stopping times:
- Case (i): $t_1 = 3\,\text{s}$
- Case (ii): $t_2 = 5\,\text{s}$

Impulse is equal to change in momentum:

$J = \Delta p = m(v-u)$

$J = 5(0-25) = -125\,\text{kg m s}^{-1}$

So, in both cases, the magnitude of impulse is

$|J| = 125\,\text{N s}$

Since the initial and final velocities are the same in both experiments, the impulse is same in both cases.

Average force is given by:

$F_{\text{avg}} = \frac{\Delta p}{\Delta t}$

$F_{\text{avg,1}} = \frac{-125}{3}\,\text{N}$

Magnitude:

$|F_{\text{avg,1}}| = \frac{125}{3} \approx 41.7\,\text{N}$

$F_{\text{avg,2}} = \frac{-125}{5} = -25\,\text{N}$

Magnitude:

$|F_{\text{avg,2}}| = 25\,\text{N}$

Thus, the average force is different in the two cases.

The correct option is B.