Question

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

• A. $\frac{\sqrt{3}}{2}g{\text{m/s}}^2$
• B. $\frac{2}{\sqrt{3}}g{\text{m/s}}^2$
• C. $g\sqrt{3}{\text{m/s}}^2$
• D. $\frac{g}{\sqrt{3}}{\text{m/s}}^2$

Answer 1

The correct option is D $\frac{g}{\sqrt{3}}{\text{m/s}}^2$

In ground frame, let acceleration of carriage is $a{\text{m/s}}^2$.
$\therefore$ Pendulum will also have acceleration $a{\text{m/s}}^2$.

$\text{T cos}\theta =mg$
$\text{T sin}\theta =ma$
From these two equations we get,
$\text{a = g tan}\theta =\text{g tan}{30}^{\circ }=\frac{g}{\sqrt{3}}{\text{m/s}}^2$