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Q.

A disc of radius R is spun to an angular speed ω0 about its axis and then imparted a horizontal velocity of magnitude ω0R4at t=0 with its plane remaining vertical. The coefficient of friction between the disc and the plane is sufficient to allow pure rolling, once it starts. The sense of rotation and direction of its linear speed are shown in the figure. Choose the correct statement.

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a

The disc will return to its initial position. 

b

the disc will stop finally irrespective of value of v and ω.

c

if v0=ω0R/2 then the disc will stop.

d

the friction will act in rightward direction after the rolling starts.

answer is A, C.

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Detailed Solution

Li=mv0R=Icω0 =0R4R-12mR2ω0=-0R24

Since Li is -ve.

it will return to its initial position.

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