Work Energy And Power Question 241

Question: A running man has half the kinetic energy of that of a boy of half of his mass. The man speeds up by 1m/s so as to have same K.E. as that of the boy. The original speed of the man will be

Options:

A) $ \sqrt{2}m/s $

B) $ ( \sqrt{2}-1 )m/s $

C) $ \frac{1}{( \sqrt{2}-1 )}m/s $

D)

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Answer:

Correct Answer: C

Solution:

[c] Let $ m=massofboy $ , $ M=massofman $

$ v=velocityofboy $ , $ V=velocityofman $

$ \frac{1}{2}MV^{2}=\frac{1}{2}[ \frac{1}{2}mv^{2} ] $ -(i)

$ \frac{1}{2}M{{( V+1 )}^{2}}=1[ \frac{1}{2}mv^{2} ] $ -(ii) $ Putting m = \frac{M}{2} and solving V= \frac{1}{\sqrt{2}-1} $



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