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Question

# A cart of mass M=100 kg is at rest over a smooth horizontal surface. A boy of mass m=50 kg is standing over the cart. If he jumps from the cart with a horizontal velocity of 20 msâˆ’1, the final velocity of the cart is :

A
10 ms1
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B
20 ms1
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C
10 ms1
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D
20 ms1
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Solution

## The correct option is C −10 ms−1Given: Mass of boy (m1) = 50 kg Mass of cart (m2) = 100 kg Initial velocity of boy (u1) = 0 ms−1 Initial velocity of cart (u2) = 0 ms−1 Final velocity of boy (v1) = 20 ms−1 Final velocity of cart (v2) = ? According to the law of conservation of momentum, Initial momentum of the system = Final momentum of the system ⇒ m1u1+m2u2=m1v1+m2v2 ⇒ 0 + 0 =50×20+100×v2 ⇒ v2=−10 ms−1 Negative sign indicates the velocity of cart is in opposite direction of the velocity of the boy.

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