An annular disk of mass M, inner radius a and outer radius b is placed on a horizontal surface with coefficient of friction \mu, as shown in the figure. At some time, an impulse J_0 \stackrel{\^}{x} is applied at a height h above the center of the disk. If h=h_m then the disk rolls without slipping along the x-axis. Which of the following statement(s) is(are) correct? [JEE Adv 2023 P2]

For \mu \neq 0 and a \to 0, h_m=b \/ 2

For \mu \neq 0 and a \to b, h_m=b

For h=h_m, the initial angular velocity does not depend on the inner radius a

For \mu=0 and h=0, the wheel always slides without rolling

Rotational Motion

Section: Physics

Question : 4 of 54

Marks: +1, -0

An annular disk of mass M, inner radius a and outer radius b is placed on a horizontal surface with coefficient of friction µ, as shown in the figure. At some time, an impulse J0

is applied at a height h above the center of the disk. If h=hm then the disk rolls without slipping along the x-axis. Which of the following statement(s) is(are) correct?

[JEE Adv 2023 P2]

For µ≠0 and a→0,hm=b∕2
For µ≠0 and a→b,hm=b
For h=hm, the initial angular velocity does not depend on the inner radius a
For µ=0 and h=0, the wheel always slides without rolling

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