A uniform disc of mass $$5$$ kg and radius $$1$$ m is placed vertically on a rough horizontal surface. A horizontal time varying force is applied on the center 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 $$=$$ $$10$$ m $$/$$ $$s2)Then$$ which of the following option $$is/are$$ correct

Question

A uniform disc of mass $$5$$ kg and radius $$1$$ m is placed vertically on a rough horizontal surface. A horizontal time varying force is applied on the center 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 $$=$$ $$10$$ m $$/$$ $$s2)Then$$ which of the following option $$is/are$$ correct

Infinity Learn · Accepted Answer

Translation : F−f $$=$$ ma−−−$$1$$​⇒Rotation : τ$$=I$$α​⇒f $$R=mR22aR$$∵$$a=R$$α​⇒$$f=ma2$$−−−$$3from$$ $$1$$ & $$3$$​⇒$$f=F3=10t3$$∵$$Ft=808$$⇒$$F=10tFor$$ pure rolling​⇒f≤μmg​⇒$$10t3$$≤$$20$$​⇒t≤$$6s$$

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