A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the circumference of A, as shown in the figure. A flat surface of B also lies on the plane of the table. The center of mass of B has fixed angular speed ω about the vertical axis passing through the center of A. The angular momentum of B is nMωR2 with respect to the center of A. Which of the following is the value of n?

Engineering

Physics

Rolling

Angular Momentum and Conservation of Angular Momentum

Question

A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the circumference of A, as shown in the figure. A flat surface of B also lies on the plane of the table. The center of mass of B has fixed angular speed ω about the vertical axis passing through the center of A. The angular momentum of B is nMωR² with respect to the center of A. Which of the following is the value of n?

$\frac{7}{2}$

$\frac{9}{2}$

LiveFree JEE Main Previous Year Online Papers Live Free JEE Advance Previous Year Online Papers

College PredictorLive

Know your College Admission Chances Based on your Rank/Percentile, Category and Home State.

Get your JEE Main Personalised Report with Top Predicted Colleges in JoSA

v = ω (2R)

v = ω₀R : no slipping

∴ ω₀ = 2ω

$\vec{L} = mr \vec{r} \times {\vec{v}}_{c} + I_{c} ω_{0}$

$M 2 Rv + \frac{1}{2} {MR}^{2} ω_{0}$

$4 {MR}^{2} ω + \frac{1}{2} {MR}^{2} (2 ω)$ = 5MR²ω

∴ n = 5