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Physics-

General

Easy

Question

A disc of mass 2 M and radius R is placed on a fixed plank (rough) of length L. The coefficient of friction between the plank and disc is $mu$ = 0.5. String (light) is connected to centre of disc and passing over a smooth light pulley and connected to a block of mass M as shown in the figure. Now the disc is given an angular velocity $omega subscript 0 end subscript$ in clockwise direction and is gently placed on the plank. Consider this instant as t=0. Based on above information, answer the following questions: Time $t subscript 0 end subscript$ 1 at which the disc will cross the other end of the plank is-

$\sqrt{\frac{8 L}{g}}$
$\frac{ω_{0} R}{g} + \sqrt{\frac{8 L}{g}}$
$\sqrt{\frac{8 L}{g}} + \frac{4 ω_{0} R}{g}$
$\sqrt{\frac{ω_{0} R}{g}} + \sqrt{\frac{4 L}{g}}$

The correct answer is: $fraction numerator omega subscript 0 end subscript R over denominator g end fraction plus square root of fraction numerator 8 L over denominator g end fraction end root$

Mg – T = Ma ...(i)T – f r = 2Ma ...(ii)

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