A horizontal force F is applied at the centre of mass of a cylindrical object of mass m and radius R, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is μ . The centre of mass of the object has an acceleration a. The acceleration due to gravity is g. Given that the object rolls without slipping, which of the following $$statement(s)$$ $$is(are)$$ correct ?

Question

A horizontal force F is applied at the centre of mass of a cylindrical object of mass m and radius R, perpendicular to its axis as shown in the figure. The coefficient of friction between the object and the ground is μ . The centre of mass of the object has an acceleration a. The acceleration due to gravity is g. Given that the object rolls without slipping, which of the following $$statement(s)$$ $$is(are)$$ correct ?

Infinity Learn · Accepted Answer

F−$$f=maf$$⋅$$R=I$$α$$a=R$$α$$FR=mR2$$α$$+I$$α ⇒α$$=FRI+mR2a=FR2I+mR2f=IFI+mR2=IaR2(B)$$ for solid cylinder $$I=mR22a=FR232mR2=2F3m$$ ⇒ $$a=fR2I=$$μ$$mgR2mR22=2$$μ$$g(C)$$ $$f=$$μ$$N=$$μmg is the limiting friction and not always the value.(D) for hollow cylinder $$a=FR22mR2$$;$$I=mR2=F2m$$

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