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Q.

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

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a

at  t = 3 sec disc is rolling without slipping

b

at  t = 4sec disc is rolling  without slipping

c

at  t = 7sec disc is rolling without slipping

d

at  t = 3sec friction force is  10N

answer is A.

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Detailed Solution

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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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