Question

In case of a simple pendulum, time period versus length is depicted by
A.
B.
C.
D.

Answer 1

Hint:In a simple pendulum the time period is defined as the time taken to complete one oscillation by the bob attached to the string. The time period is depending only on the length of the pendulum. By using the relation between the time period and the length of the pendulum we can easily draw the graph between them.

Formula used:
The time period (T) of a simple pendulum is given as,
\[T = 2\pi \sqrt {\dfrac{l}{g}} \]
where l is the length of a simple pendulum and g is the acceleration due to gravity.

Complete step by step solution:
For a simple pendulum, time period is given as
\[T = 2\pi \sqrt {\dfrac{l}{g}} \]
From this equation, we get the relation between time period(T) and the length (l) of the simple pendulum.
\[T \propto \sqrt l \]
\[\therefore {T^2} \propto l\]
Here the time period is directly proportional to the square root of the length of a simple pendulum. It means if the time period increases then length will also increase. So, the graph of time period versus length shown must show increments of both.

Hence option B is the correct answer.

Note: The simple pendulum is a system which moves in an oscillatory motion. The simple pendulum exhibits simple harmonic motion (or SHM) in which the acceleration (a) of the bob of a pendulum is directly proportional to the displacement(x) from the mean position and it is always directed towards it. The time period (T)of the simple pendulum is dependent on the length of the pendulum and independent of the amplitude of oscillation.