Question

A man measures time period of a pendulum $(T)$ in stationary lift. If the lift moves upward with acceleration $\frac{g}{4},$ then new time period will be

• A. $\frac{2T}{\sqrt{5}}$
• B. $\frac{\sqrt{5}T}{2}$
• C. $\frac{\sqrt{5}}{2T}$
• D. $\frac{2}{\sqrt{5}T}$

Answer 1

Answer: (A)

$\frac{2T}{\sqrt{5}}$

Answer 2

$T = 2\pi\sqrt{\frac{l}{g}}$ ⇒ $\frac{T^{'}}{T} = \sqrt{\frac{g}{g^{'}}} = \sqrt{\frac{g}{g + \frac{g}{4}}} = \sqrt{\frac{4}{5}} = \frac{2}{\sqrt{5}}$