Question

Find out the effective length of a simple pendulum suspended at a place of $\text{g}=9.8{\text{m s}}^{-2}$, with a time period of $1\text{min}$.

• A. $56\text{km}$
• B. $56\text{m}$
• C. $5.6\text{km}$
• D. $560\text{m}$

Answer 1

The correct option is C $5.6\text{km}$

Given:
The time period of the pendulum, $\text{T}=1\text{min}=60\text{s}$
Acceleration due to gravity, $\text{g}=9.8{\text{m s}}^{-2}$
Let the effective length of the pendulum be $\text{l}$.
Time period of a pendulum, $\text{T}=2\pi \sqrt{\frac{\text{l}}{\text{g}}}$
$⟹\text{l}=\text{g}\frac{{\text{T}}^2}{2\pi }=\frac{9.8\times 60\times 60}{2\pi }$
$=\frac{35280}{2\pi }=5614.97\text{m}\approx 5.6\text{km}$