Question

What will be the value of the frequency of a simple pendulum in a gravity free space?
A. Zero
B. Infinity
C. Unity
D. 5

Answer 1

A pendulum is a weight that is suspended from a pivot and may freely swing. When a pendulum is pushed sideways from its resting, equilibrium position, gravity acts as a restorative force, accelerating the pendulum back to its equilibrium position. The restoring force acting on the mass of the pendulum causes it to oscillate about the equilibrium position, swinging back and forth, when it is released. The period is the amount of time it takes to complete one complete cycle, which includes both a left and right swing. We use this concept here.

Formula used:
${{T = 2\pi }}\sqrt {\dfrac{{\text{l}}}{{\text{g}}}}$
Here, $T$ = time period, $L$ =length of the string and $G$ = acceleration due to gravity.

Complete step by step answer:
A simple pendulum is described as having a point mass, also known as the pendulum bob, hung on a string with negligible mass of length $L$. The only forces operating on the bob are gravity (i.e., the bob's weight) and string tension. In comparison to the mass of the bob, the mass of the string is believed to be insignificant.

A basic pendulum's period is determined by its length and gravity's acceleration. The period is expressed as and is totally independent of other parameters like mass and maximum displacement.Now given g = 0.
Hence ${{T = 2\pi }}\sqrt {\dfrac{{\text{l}}}{0}}$ which can be understood as $T$ tends to infinity, We know that the Frequency Is the inverse of time,
$f = \dfrac{1}{T}$
$\Rightarrow f = \dfrac{1}{{\dfrac{1}{0}}}$
$\therefore f = 0$
Hence it Frequency becomes zero.

Hence, the correct answer is option A.

Note: The relation between Frequency and Time period should be noted and memorised. The number of times a recurring event occurs per unit of time is known as frequency. It's also referred to as temporal frequency to distinguish it from spatial frequency, and ordinary frequency to distinguish it from angular frequency.