Work Energy And Power Question 303

Question: Two identical balls A and B are released from the positions shown in figure. They collide elastically on horizontal portion $ M/N $ . All surfaces are smooth. The ratio of heights attained by A and B after collision will be

Options:

A) $ 1:4 $

B) $ 2:1 $

C) $ 4:13 $

D) $ 2:5 $

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Answer:

Correct Answer: C

Solution:

[c] After collision, balls exchange their velocities

$ \therefore $ $ V _{A}=\sqrt{2gh} $

and $ V _{B}=\sqrt{2g(4h)}=2\sqrt{2gh} $

Height gained by A will be $ h _{A}=h $

But path of B will be first straight line and then parabolic as shown in figure

After calculation, we can show that $ h _{B}=\frac{13}{4}h $

$ \therefore $ $ \frac{h _{A}}{h _{B}}=\frac{4}{13} $



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