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Question

# Block A is placed on a rough wedge B which is placed on a smooth surface. The wedge has angle of inclination of 30o and is imparted a horizontal acceleration g towards right. Block A is given an initial velocity v0 along w.r.t. incline. Find the coefficient of friction for which block A moves with constant velocity v0 with respect to wedge (g=10m/s2).

A
(31)(3+1)
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B
(21)(2+1)
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C
(22)(2+2)
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D
(33)(3+3)
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Solution

## The correct option is A (√3−1)(√3+1)As shown in fig. ma is pseudo force towars left.If block A moves with constant velocity then net force is zero.Force along the surface of bock B is;macosθ=f+mgsinθ ..................(1)where f− frictional forceforce opposite to the movement of block ALet μ= coefficient of frictional force N=masinθ+mgcosθ(1) becomes;macosθ=μ(masinθ+mgcosθ)+mgsinθwhere a=g,θ=30∘mgcos30∘=μ(mgsin30∘+mgcos30∘)+mgsin30∘g(√32)=μ(g2+√3g2)+(g2)μ(1+√32)=√3−12μ=√3−1√3+1

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