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

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 $n M ω R^{2}$ with respect to the center of A. Which of the following is the value of $n$ [2022]

Smart Achievers · Accepted Answer

(2)

$We have V = (2 R) ω$

$As B is rolling on circumference of A.$

$So, V = ω' R$

$\Rightarrow 2 R ω = ω' R$

$\Rightarrow ω' = 2 ω$

$So, \vec{L} w.r.t COM of A$

$= (I ω' + m (2 R) V) \hat{k}$

$= (\frac{1}{2} M R^{2} (2 ω) + m (2 R) (2 R ω)) \hat{k} = 5 M R^{2} ω \hat{k}$

$So, n = 5$

Solution

1 $2$

2 $5$

3 $\frac{7}{2}$

4 $\frac{9}{2}$

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Solution

1 2

2 5

3 72

4 92

Ans. (2) We have V=(2R)ω As B is rolling on circumference of A. So, V=ω'R ⇒2Rω=ω'R ⇒ω'=2ω So, L→ w.r.t COM of A =(Iω'+m(2R)V)k^ =(12MR2(2ω)+m(2R)(2Rω))k^=5MR2ωk^ So, n=5

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1 $2$

2 $5$

3 $\frac{7}{2}$

4 $\frac{9}{2}$