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Q.

A plank having mass M is placed on smooth horizontal surface. Block of mass m is placed on it coefficient of friction between block and plank is μ0+kx2, where k is constant and x is relative displacement between block and plank. A force F is applied on block where F = at, where a = 10; t is in second. Find t0 when relative motion will occur between block and plank

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a

μ0M+μ0M2m

b

μ0m+μ0M2m

c

μ0m+μ0m2M

d

μ0M+μ0m2M

answer is C.

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Detailed Solution

Let at time t0 relative motion will occurμ0mg=Ma    ......(1)10 t0−μ0mg=ma   .......(2)From (1) and (2) ; t0=μ0m+μ0m2M
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A plank having mass M is placed on smooth horizontal surface. Block of mass m is placed on it coefficient of friction between block and plank is μ0+kx2, where k is constant and x is relative displacement between block and plank. A force F is applied on block where F = at, where a = 10; t is in second. Find t0 when relative motion will occur between block and plank