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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).
693991_03fe7266fa67456db2f8d476f1f7ddc0.png

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 (31)(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 force

force opposite to the movement of block A

Let μ= coefficient of frictional force

N=masinθ+mgcosθ

(1) becomes;
macosθ=μ(masinθ+mgcosθ)+mgsinθ

where a=g,θ=30

mgcos30=μ(mgsin30+mgcos30)+mgsin30

g(32)=μ(g2+3g2)+(g2)

μ(1+32)=312

μ=313+1

980950_693991_ans_b0b5ff0016084285a290d2f836f4a3b2.png

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