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Q.

A solid cylinder of mass m is wrapped with an inextensible light string and, is placed on a rough inclined plane as shown in the figure. The frictional force acting between the cylinder and the inclined plane is:[The coefficient of static friction, μS is 0.4]

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a

0

b

mg5

c

5 mg

d

72mg

answer is B.

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Detailed Solution

Translational Equilibrium mgsinθ=T+f  ----------(1)Rotational Equilibrium (about CM)T×R=f×R ⇒T=f----(2)  ⇒f=mgsin602=34mg=0.433mgBut maximum frictional fore is fmax=μmgcos60  =  0.2mgApplied force in greater than maximum static frictional force.So, friction = 0.2 mg=15mg
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