Question

What is the length of Second’s pendulum if g is $980\,cm/{s^2}$ ?

A.102.4 cm
B.99.2 cm
C.88 cm
D.78 cm

Answer 1

Hint: In this question we will come across topics like pendulums that are of two types namely simple and compound pendulum. We will be learning about both and the concepts behind them which will help us in approaching our solution.

Complete answer:
Pendulum: Is any weight that is hanged from a pin to let it oscillate freely. When the pendulum is moved sideways from its equilibrium point. At that time, it feels a restoring force which forces the pendulum back to equilibrium point.
Simple Pendulum: A simple pendulum is a perfect mathematical model of a pendulum. In this a weight also called as bob is connected to the end of a massless string suspended from a pin point, without friction. When given an initial push, it will swing left and right at the same amplitude.
Second’s pendulum: Is that pendulum which provides us a period of explicitly two seconds. In one second, it swings in one direction and in another one second it would return from the swing.

As of now we know what the second pendulum is. It is that pendulum which provides us a period of explicitly two seconds. In one second, it swings in one direction and in another one second it would return from the swing.
 So, the time period that comes out to be
\[T = 2s\]
We all know the formula of time period of simple pendulum:
\[T = 2\pi \sqrt {\dfrac{l}{g}} \]
Now by squaring both the sides we get:
\[ \Rightarrow l = \dfrac{{{T^2}g}}{{4{\pi ^2}}}\]
\[ = \dfrac{{{2^2} \times 980}}{{4{\pi ^2}}}\]
Hence the answer comes out by solving it is:
\[ = 99.29 \cong 99.2cm\]
\[ \cong 99.2\]

Hence, the correct option is B - $99.2cm$

Note: To complete one whole swing pendulum requires a certain period of time that is called a time period of pendulum.
Time period is usually concerned and gets affected by length and the strength of gravity. Remember there is no effect in time period if we change the mass of the hanged object.