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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 fixed rough inclined surface for which the coefficient of friction is μ=34. The block of mass m is initially at rest. The block of mass M is released from rest with spring in unstretched state. The minimum value of M required to move the block up the plane is(neglect mass of string and pulley and friction in pulley.)

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a

35m

b

45m

c

65m

d

32m

answer is A.

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Detailed Solution

As long as the block of mass m remains stationary, the block of mass M released from rest let it comes down by distance x, applying conservation of mechanical energy  ΔK+ΔU=0⇒0+ΔUgravity +ΔUspring =0−Mgx+12kx2=0⇒x=2MgkThus at the maximum extension in spring is   kx=2Mg   ……(i)For block of mass m to just move up the inclinekx=mgsin⁡θ+μmgcos⁡θ  ……..(ii)   2Mg=mg×35+34mg×45M=35m
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