Answer

Verified

53.4k+ views

**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.

Recently Updated Pages

Why do we see inverted images in a spoon class 10 physics JEE_Main

A farsighted man who has lost his spectacles reads class 10 physics JEE_Main

State whether true or false The outermost layer of class 10 physics JEE_Main

Which is not the correct advantage of parallel combination class 10 physics JEE_Main

State two factors upon which the heat absorbed by a class 10 physics JEE_Main

What will be the halflife of a first order reaction class 12 chemistry JEE_Main

Other Pages

The nitride ion in lithium nitride is composed of A class 11 chemistry JEE_Main

The resultant of vec A and vec B is perpendicular to class 11 physics JEE_Main

A given ray of light suffers minimum deviation in an class 12 physics JEE_Main

Electric field due to uniformly charged sphere class 12 physics JEE_Main

Oxidation of succinate ion produces ethylene and carbon class 12 chemistry JEE_Main

when an object Is placed at a distance of 60 cm from class 12 physics JEE_Main