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