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Q.

A light rod with the balls A and B is clamped at the centre in such a way that it can rotate freely about a horizontal axis through the clamp. The system is kept at rest in the horizontal position. A particle P of the same mass m is dropped from a height h on the ball B. The particle collide with B and sticks to it. Find the minimum value of h for which the rod will make a complete revolution after the collision.

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a

h = 32L

b

h = 45L

c

h = 3 L

d

h = 23L

answer is D.

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Detailed Solution

The velocity of the particle + ball B before collision

v = 2gh

The velocity of the particle + ball B after collision

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v'  =  m2gh+0m+m      =  gh2

For the full rotation to occur, ball B will reach to the highest point, and so

           Ki + Ui                  =  Kf + Uf 12m+mv'2+12mv'2+ 0  = 0 + 2mgL2- mg L2

After substituting the value of v' and simplifying, we get

               h = 2L3

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