JEE Advanced 2022 · Paper 2 · Physics Q15

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PhysicsSingle correct+3 / -1Question 33 of 54

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 $\omega$ about the vertical axis passing through the center of $A$ . The angular momentum of $B$ is $nM\omega R^2$ with respect to the center of $A$ . Which of the following is the value of $n$ ?

Top view: disk A (shaded, fixed, labelled A) and disk B (unshaded, labelled B) of equal radius touching externally at one point, B above and to the right of A. A curved arrow above B shows B moving counter-clockwise around A.

2

5

\frac72

\frac92

Answer and worked solution

Official answer: B

Spin of B. The point of contact is at rest, and the centre of B moves on a circle of radius $2R$ at $\omega$ , so its speed is $2R\omega$ . Rolling without slipping then gives B a spin of
$\omega_s=\frac{2R\omega}R=2\omega.$

Angular momentum about the centre of A.
$L=M(2R)^2\omega+\frac12MR^2(2\omega)=4MR^2\omega+MR^2\omega=5MR^2\omega.$
So $n=5$ . (B).

Topics:Angular momentum and its conservation Rolling motion

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JEE Advanced 2022 · Paper 2, Physics question 15