JEE Advanced2023PhysicsRotational MotionActual
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 J 0 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?
Options
- AFor μ ≠ 0 and a → 0 ,   h m = b 2
- BFor μ ≠ 0 and a → b ,   h m = b
- CFor h = h m , the initial angular velocity does not depend on the inner radius a
- DFor μ = 0 and h = 0 , the wheel always slides without rolling
Correct answer
A. For μ ≠ 0 and a → 0 ,   h m = b 2
Step-by-step solution
As we know, J → = ∆ P → ⇒   J 0 = M V                             . . .   i About center of the disk, we can also write J 0 × h = I C M ω ⇒   J 0 × h = M 2 a 2 + b 2 ω                             . . .   i i If h = h m ⇒ ω = V b pure rolling From equation(ii), we can write ⇒   J 0 &