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Q.

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=3/4.. The minimum value of M required to move the block up the plane is (neglect mass of string and pulley and friction is pulley).

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a

35m

b

45m

c

2m

d

32m

answer is A.

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Detailed Solution

mgsin⁡θ=35mgfmax=μmgcos⁡θ=3445mg=35mgfmax=mgsin⁡θ=35mgBlock will move upwards when kx0=fmax+mgsin⁡θ=65mg ……..(i)From conservation of mechanical energy Mg⁡x0=12kx02M=kx02g=65mg2g=35m
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