Question

The period of pendulum depends upon
A. Mass
B. Length
C. Amplitude
D. Energy

Answer 1

Here, by period it is meant time period. So, to answer this question, use the mathematical expression for the time period of a pendulum. Observe this mathematical expression and find out on which quantity out of these given options the time period of the pendulum depends.

Formula used:
$T= 2 \pi \sqrt {\dfrac {l}{g}}$

Complete solution:
Pendulum is based on the principle that when it is moved or displaced sideways from its resting equilibrium position, it is subjected to a restoring force due to gravity. Due to this force the pendulum is accelerated back towards its equilibrium position.
Time period of a pendulum is defined as the time taken by the pendulum to make a complete oscillation. Time period of a pendulum is given by,
$T= 2 \pi \sqrt {\dfrac {l}{g}}$
Where,
T is the time period
l is the length of the string
g is the acceleration due to gravity
From the above equation, it is evident that the time period of the pendulum is dependent on the length of the string and acceleration due to gravity.
Thus, the period of the pendulum depends upon length.

So, the correct answer is option A i.e. length.

Note:
In general, the time period of a pendulum means one complete cycle that is one complete left string and a complete right string. Students must remember that the time period for a pendulum is not the same as the time period for simple harmonic motion even though both exhibit periodic motion. Time period for a simple harmonic motion depends on the mass of the object but the time period for a pendulum does not depend on the mass of the object.