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Q.

A weightless rod of length l with a small load of mass m at one of its end is held vertical with its lower end hinged on a horizontal surface. The load touches a wedge right sets the system in motion (see figure), with rod rotating freely in vertical plane about its lower end. There is no friction. If the rod forms an angle θ=π3 with the vertical at the moment the load separates from the wedge, then

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a

The speed of the wedge at that moment will be gl8

b

The mass ration Mm=3

c

The mass ratio Mm=4

d

The speed of the bob at that moment will be gl2

answer is B, C, D.

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Detailed Solution

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mgl2=12mV12+M8V12

V12l32=g34,    V12=gl2

mgl2=mgl4+M16gl

14m=M16 

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A weightless rod of length l with a small load of mass m at one of its end is held vertical with its lower end hinged on a horizontal surface. The load touches a wedge right sets the system in motion (see figure), with rod rotating freely in vertical plane about its lower end. There is no friction. If the rod forms an angle θ=π3 with the vertical at the moment the load separates from the wedge, then