Q.

A 45 kg girl and her 60 kg brother are at rest at the center of a frozen pond (μ=0) almost touching each other. He pushes her so that she slides away relatively at 5.6 ms-1. Assume that he extends his hands by 60 cm to complete the push and that he applies a constant horizontal force F on his sister.

Moderate

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a

The girl will be moving at a speed of 2.4 ms-1 at the end of the push.

b

The girl will be moving at a speed of 3.2 ms-1 at the end of the push.

c

F=627 N

d

The push completes in nearly 486 ms

answer is 2.

(Detailed Solution Below)

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Detailed Solution

Conserving momentum we get45×vG=60×vBvG+vB=5.6ms−1⇒vG=3.2ms−1 &vB=2.4ms−1 Force =KEsrel=12mBvB2+12mava20.6=672N Time of push =mBvBF=60×2.462=285.7ms

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