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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 5.6ms−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.

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a

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

b

The boy will be moving at a speed of  3.2ms−1  at the end of the push.

c

F=627N

d

The push completes in nearly 214.3 ms

answer is D.

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Detailed Solution

Conserving momentum we get45×vG=60×vBvG+vB=5.6  ms−1vG=3.2  ms−1 & vB=2.4  ms−1Applying, work energy theorem W=△K⇒Force = KEsrel=12mBvB2+12mGvG2srel= 672 NTime of push =  mBvBF=60×2.4672=0.2143 s = 214.3 ms
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