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Q A solid cylinder of mass m and radius r is rolling on a rough inclined plane of inclination θ. The coefficient of friction between the cylinder and incline is m. Then (A) frictional force is always mmg cos θ (B) friction is a dissipative force (C) by decreasing θ, frictional force decreases (D) friction opposes translation and supports rotation

  A solid cylinder of mass m and radius r is rolling on a rough inclined plane of inclination θ. The coefficient of friction between the cylinder and incline is m. Then


        (A)    frictional force is always mmg cos θ


        (B)    friction is a dissipative force


        (C)    by decreasing θ, frictional force decreases


        (D)    friction opposes translation and supports rotation

Grade:Upto college level

1 Answers

Badiuddin askIITians.ismu Expert
147 Points
11 years ago

Dear Mainak

 

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N = mgcosx

maximum frictional force  f= μN =μmgcosx

 this friction force will not always act .it is the maximum possible frictional force.

 a= (mgsinx -f)/m

for pure rollinr  α =a/r

 

and torque f.r  = mr2/2 α

                 f  =ma/2

                    =m/2 (mgsinx -f)/m

                f = mg/3 sinx

by decresing x frictional force decreses

 so  d option is correct

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