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Question

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
mhtanθMm
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C
mhcotθM+m
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D
mhcotθMm
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Solution

The correct option is C mhcotθM+m

Here, the system is wedge + block.

Net force on the system in horizontal direction (i.e x-direction) is zero, therefore, the centre of mass of the system will not move in xdirection.

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 =(hcotθx)

and,

mR= mass of block moving towards right =m

Substituting all these values in equation (i), we get,

m(hcotθx)=xM

x=mhcotθM+m

Hence, (C) is the correct option.

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