Question

The length of second pendulum is:
A) $100\,cm$
B) $99\,cm$
C) $99.4\,cm$
D) $98\,cm$

Answer 1

Hint: Use the formula of the time period of the pendulum and substitute the value of the length of the pendulum as $2\,s$ and the acceleration due to gravity as $9.8$. The obtained equation is simplified, to obtain the value of the length of the pendulum.

Formula used:
The time period is given by
$T = 2\pi \sqrt {\dfrac{l}{g}} $
Where $T$ is the time period of the pendulum, $l$ is the length of the pendulum and $g$ is the acceleration due to gravity.

Complete step by step solution:
It is known that the time period of the second pendulum is $2\,s$ .

Using the formula of the time period ,
$T = 2\pi \sqrt {\dfrac{l}{g}} $
Substituting the values of the time period of the pendulum as $2\,s$ and the acceleration due to gravity as the $9.8\,m{s^{ - 2}}$ in the above formula.
$2 = 2\pi \sqrt {\dfrac{l}{{9.8}}} $
By grouping the known parameters in one side and the unknown parameter in the other side.
$\sqrt l = \dfrac{{2 \times \sqrt {9.8} }}{{2\pi }}$
By taking a square on both sides of the equation, to find the value of the length of the pendulum.
$l = \dfrac{{4 \times 9.8}}{{4{\pi ^2}}}$
By the simplification of the above step,
$l = \dfrac{{9.8}}{{{\pi ^2}}}$
It is known that the value of the $\pi = 3.14$ in the above step,
$l = \dfrac{{9.8}}{{{{3.14}^2}}}$
By the further simplification,
$l = 0.994\,m$
All the options given in the question contain the units in the centimeter. But the obtained answer is in meters. So the obtained answer is converted into the centimeter unit.
$l = 99.4\,cm$

Thus the option (C) is correct.

Note: When the pendulum swings from one side to the other side, it takes two seconds to reach the other side. Since the pendulum takes the same time, but the maximum distance is covered at the high speed and the minimum distance is covered at the low speed.