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 w. The pendulum sill hang at an angle q with the vertical such that :-

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

Answer 1

The correct option is 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 bob is at rest

$\therefore T\sin \theta =m{a}_r\left(a_r=r{w}^2\right)$

$\Rightarrow T\sin \theta =mr{w}^2$---------------$\left(1\right)$

$T\cos \theta =mg$------------------------$\left(2\right)$

Dividing $\left(2\right)$ by $\left(1\right)$ we get $\tan \theta =\frac{r{w}^2}{g}$

Hence

option $\left(C\right)$ is correct answer.