@Pranjal Jain
–
\(\text{angular velocity}=\dfrac{\text{Relative velocity perpendicular to line joining them}}{\text{Distance between them}}\)

By simple geometry, \(\angle AOP=30^\circ\)

Case I: \(A\) is fixed to ground, so, the velocity of \(P\) will be \(\omega R\) at angle \(120^\circ\) to the line joining \(AP\), thus, \(\omega_1=\dfrac{\omega R\cos 30^\circ}{\sqrt{3}R}\)

Case II: \(A\) is fixed to disc, in this case, velocity of \(A\) will add up in relative velocity. In this case also, velocity of \(A\) will be \(\omega R\) at angle \(60^\circ\) to the line joining \(AP\). Thus, \(\omega_2=\dfrac{\omega R\cos 30^\circ+\omega R\cos 30^\circ}{\sqrt{3}R}=2\omega_1\Rightarrow \dfrac{\omega_1}{\omega_2}=\dfrac{1}{2}\)

Easy Math Editor

`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

Sort by:

TopNewest@Raghav Vaidyanathan the problem is in the middle.

Log in to reply

I have rotated the image. \(\huge\ddot\smile\)

Log in to reply

U can tell me the solution . ???

Log in to reply

Log in to reply

By simple geometry, \(\angle AOP=30^\circ\)

Case I:\(A\) is fixed to ground, so, the velocity of \(P\) will be \(\omega R\) at angle \(120^\circ\) to the line joining \(AP\), thus, \(\omega_1=\dfrac{\omega R\cos 30^\circ}{\sqrt{3}R}\)Case II:\(A\) is fixed to disc, in this case, velocity of \(A\) will add up in relative velocity. In this case also, velocity of \(A\) will be \(\omega R\) at angle \(60^\circ\) to the line joining \(AP\). Thus, \(\omega_2=\dfrac{\omega R\cos 30^\circ+\omega R\cos 30^\circ}{\sqrt{3}R}=2\omega_1\Rightarrow \dfrac{\omega_1}{\omega_2}=\dfrac{1}{2}\)Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply

Log in to reply