Question

If the time period of a simple pendulum suspended at a place having $g=9.8m{s}^{-2}$ as the acceleration due to gravity is $T$, the effective length of the pendulum, $l$ is given by:

• A. $0.4372T^2$
• B. $2.3311T^2$
• C. $0.2482T^2$
• D. $1.8865T^2$

Answer 1

The correct option is C $0.2482T^2$

The time period of a simple pendulum is given by:
$T=2\pi \sqrt{\frac{l}{g}}$ ----- (1)
where, $l$ is the effective length of the pendulum, $g$ is the acceleration due to gravity at that place.
On squaring on both sides of equation (1), we get:
$T^2=4{\pi }^2\frac{l}{g}$
$⟹g{T}^2=4{\pi }^{2}l$
$⟹l=\frac{g{T}^2}{4{\pi }^2}$
$4{\pi }^2=39.4784⟹l=\frac{g{T}^2}{39.4784}$
$⟹l=0.02533g{T}^2$
Substituting g = $9.8m{s}^{-2}$, we get:
$l=0.02533\times 9.8T^2=0.2482T^2$.