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Question

A block of mass m is attached with a massless spring of force constant k. The block is placed over a rough inclined surface for which the coefficient of friction is μ=34. The minimum value of M required to moved the block up the plane is (Neglect mass of pulley, string and friction in pulley).


A
35m
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B
45m
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C
65m
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D
32m
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Solution

The correct option is A 35m
Given, coefficient of friction μ=34,
mass of block A=M,
mass of block B=m
When block A moves for a distance x, then spring will stretch to same x value. And at that value of x, let block B be just about to move.
FBD for block B,


Block B is about to move upwards along the wedge, hence friction force will act opposite to it (downwards) along the wedge. Friction will be limiting because we want the minimum value of M.
So, kx=mgsinθ+f
kx=mgsin37+μmgcos37
kx=mg(35)+34×mg×45
kx=65mg.....(1)
For Block A,
Applying work energy theorem,
Decrease in potenital energy of A= Potential energy stored in spring
12kx2=Mgx
kx=2Mg.....(2)

Now, from eq (1) & (2), we get
M=35m is the minimum value of M required to move the block B

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