Question

Time period of a simple pendulum is $T$ inside a lift when the lift is stationary. If the lift moves upward with an acceleration $g/2$, the time period of the pendulum will be:

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

Answer 1

The correct option is C $\sqrt{\frac{2}{3}}T$

When the lift is stationary,
$T=2\pi \sqrt{\frac{L}{g}}$
A pseudo force will act downwards when the lift is accelerating upwards.
$\Rightarrow g_{eff}=g+\frac{g}{2}=\frac{3g}{2}$

$\therefore$ New time period $T^{\prime }=2\pi \sqrt{\frac{L}{g_{eff}}}=2\pi \sqrt{\frac{2L}{3g}}$
$\therefore T^{\prime }=\sqrt{\frac{2}{3}}T$

Hence, option (c) is correct.