Question

A boy holds a pendulum in his hand while standing at the edge of a circular platform of radius $r$ rotating at an angular speed $\omega$. The pendulum will hang at an angle $\theta$ with the verticle such that

• A. $tan\theta =0$
• B. $tan\theta =\frac{{\omega }^2{r}^2}{g}$
• C. $tan\theta =\frac{r{\omega }^2}{g}$
• D. $tan\theta =\frac{g}{{\omega }^{2}r}$

Answer 1

Answer: (C)

$tan\theta =\frac{r{\omega }^2}{g}$

A pseudo force $\left(m{a}_r\right)$ acts on the bob due to the rotation of circular platform.

In bob's frame, the bob is at rest (or equilibrium).

$\therefore$ $Tsin\theta =m{a}_r$ where $a_r=r{w}^2$

$⟹$ $Tsin\theta =mr{w}^2$ ........(1)

Also $Tcos\theta =mg$ ..........(2)

Divide (2) by (1) we get, $tan\theta =\frac{r{w}^2}{g}$