Questions

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 ${\mathrm{\mu }}_{0}+{\mathrm{kx}}^{2}$, 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 ${\mathrm{t}}_{0}$ 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

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detailed solution

Correct option is C

Let at time t0 relative motion will occurμ0mg=Ma    ......(1)10 t0−μ0mg=ma   .......(2)From (1) and (2) ; t0=μ0m+μ0m2M

A 40 kg slab rests on a frictionless floor as shown in the figure. A l0 kg block rests on the top of the slab. The static coefficient of friction between the block and slab is 0.60 while the kinetic friction is 0.40. The l0 kg block is acted upon by a horizontal force 100 N. If g = 9.8 $\mathrm{m}/{\mathrm{s}}^{2}$, the resulting acceleration of the slab will be