A uniform disc of mass $$5kg$$ and radius $$1m$$ is placed vertically on a rough horizontal surface. A horizontal time varying force is applied on the centre of disc and its variation with time is shown in the graph. The $$co-efficient$$ of friction between disc and surface is $$0.4(Take$$ $$g=10m/s2)Then$$ which of the following option $$is/are$$ correct

Question

A uniform disc of mass $$5kg$$ and radius  $$1m$$ is placed vertically on a rough horizontal surface. A horizontal time varying force is applied on the centre of disc and its variation with time is shown in the graph. The $$co-efficient$$ of friction between disc and surface is  $$0.4(Take$$ $$g=10m/s2)Then$$ which of the following option $$is/are$$ correct

Infinity Learn · Accepted Answer

From graph , F as function of time is $$F=10tTranslation$$ : $$F-f$$ $$=$$ ma Rotation : f $$R=mR22aR$$ ⇒$$f=ma2$$ ⇒$$f=F3=10t3$$ For pure rolling f≤μmg ⇒$$10t3$$≤$$20$$ ⇒t≤$$6s$$ Means , slipping will start after $$6$$ $$sec$$.  Since, $$f=10t3$$ Put $$t=3$$ $$sec$$, ⇒$$f=10$$ N

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