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 $0.4 (T a k e g = 10 m / s^{2})$
Then which of the following option is/are correct

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at t = 7sec disc is rolling without slipping

at t = 3 sec disc is rolling without slipping

at t = 3sec friction force is 10N

at t = 4sec disc is rolling without slipping

answer is A, B, D.

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Detailed Solution

$F r o m g r a p h, F a s f u n c t i o n o f t i m e i s F = 10 t$

$T r a n s l a t i o n : F - f = m a R o t a t i o n : f R = \frac{m R^{2}}{2} \frac{a}{R} \Rightarrow f = \frac{m a}{2} \Rightarrow f = \frac{F}{3} = \frac{10 t}{3} F o r p u r e r o l l i n g f \leq μ m g \Rightarrow \frac{10 t}{3} \leq 20 \Rightarrow t \leq 6 s M e a n s, s l i p p i n g w i l l s t a r t a f t e r 6 s e c . S i n c e, f = \frac{10 t}{3} P u t t = 3 s e c, \Rightarrow f = 10 N$