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A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a<R) by applying a force F at its centre ‘O’ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is:

a
Mg1−a2R2
b
Mg1−R−aR2
c
MgRR−a2−1
d
MgaR

detailed solution

Correct option is B

Assume no slipping about PTorque of F about P> torque of gravity⇒FR>Mgx​⇒FR>MgRsinθ​⇒Fmin=Mgsinθ=MgxR=MgR2−R−a2Rfrom figure opp=Hyp2−adj2​=MgR2−R−a2R2=Mg1−R−aR2

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