A block of mass m is released from the top of a wedge of mass M as shown in the figure. Find the displacement of the wedge on the horizontal ground, when the block reaches the bottom of the wedge.
Neglect friction everywhere.
A
mhtanθM+m
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B
mhtanθM−m
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C
mhcotθM+m
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D
mhcotθM−m
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Solution
The correct option is CmhcotθM+m
Here, the system is wedge + block.
Net force on the system in horizontal direction (i.ex-direction) is zero, therefore, the centre of mass of the system will not move in x−direction.
We can apply,
xRmR=xLmL...(i)
Let,
xL= displacement of wedge towards left =x
mL= mass of wedge moving towards left =M
xR= displacement of block with respect to ground towards right =(hcotθ−x)
and,
mR= mass of block moving towards right =m
Substituting all these values in equation (i), we get,