Two balls each of mass 1 kg moving in opposite directions with speed 15 m/s collides and rebounds with the same speed. The magnitude of impulse imparted to each ball due to other is

Collisions

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15 kg m s⁻¹

5 kg m s⁻¹

30 kg m s⁻¹

10 kg m s⁻¹

Solution:

Let the mass of each ball be $m = 1$ kg.

Let the initial velocity of one ball be $\vec{v}_i = +15$ m/s.

Since it rebounds with the same speed in the opposite direction, its final velocity is $\vec{v}_f = -15$ m/s.

Impulse imparted to this ball is the change in its momentum:

$\vec{J} = \Delta \vec{p} = m\vec{v}_f - m\vec{v}_i$

$\vec{J} = m(\vec{v}_f - \vec{v}_i) = 1 \times (-15 - 15) = 1 \times (-30) = -30$ kg m/s.

The magnitude of the impulse is $|\vec{J}| = |-30|$ kg m/s = 30 kg m/s.

Similarly, for the other ball, if its initial velocity was $-15$ m/s, its final velocity would be $+15$ m/s. The impulse would be $1 \times (15 - (-15)) = 1 \times (15 + 15) = 30$ kg m/s. The magnitude is the same.

Thus, the magnitude of impulse imparted to each ball is 30 kg m s⁻¹.

Two balls each of mass 1 kg moving in opposite directions with speed 15 m/s collides and rebounds with the same speed. The magnitude of impulse imparted to each ball due to other is

Solution:

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