Question

The pendulum hanging from a ceiling of a railway carriage makes angle ${30}^o$ with the vertical, when it is accelerating. The acceleration of the carriage is:

• A. $\frac{\sqrt{3}}{2}g$
• B. $\frac{2}{\sqrt{3}}g$
• C. $g\sqrt{3}$
• D. $\frac{g}{\sqrt{3}}$

Answer 1

The correct option is D $\frac{g}{\sqrt{3}}$

Given that,

Angle = ${30}^0$

Now, according to diagram

$ma\cos \theta =mg\sin \theta$

$\tan \theta =\frac{a}{g}$

$\tan \theta =\frac{a}{g}$

$a=g\tan {30}^0$

$a=g\times \frac{1}{\sqrt{3}}$

$a=\frac{g}{\sqrt{3}}$

Hence, the acceleration is $\frac{g}{\sqrt{3}}$