Question

Assertion: A girl is sitting on a swing, another girl sits by her side. There is no effect on periodic time of the swing.
Reason: The periodic time is independent of the mass but depends upon length of pendulum and acceleration due to gravity at a place, which are not affected by sitting another girl on a swing.

Answer 1

Hint: Here, two girls are sitting on a swing. A pendulum is a mass suspended from a fixed support so that it oscillates back and forth. Here, the swing acts as a pendulum. The time period of a pendulum is given in terms of length and acceleration due to gravity. From the above relation, we can determine whether the time period of the pendulum depends on the mass or not.
Formula used:
\[T=2\pi \sqrt{\dfrac{L}{g}}\]

Complete answer:
A mass \[m\] suspended by a wire of length \[L\] is called a simple pendulum. Hence, here the swing acts as a pendulum. We know that,
Time period of a pendulum, \[T=2\pi \sqrt{\dfrac{L}{g}}\]
Where, \[L\] is the length of the pendulum.
\[g\]is the acceleration due to gravity.
From the above equation, we can see that the periodic time depends upon the length of the pendulum and acceleration due to gravity and it doesn’t depend on the mass.
Hence, the time period of swing doesn’t get affected by sitting another girl on a swing.
Therefore, both assertion and reason are correct.

Note:
From the time period equation of a pendulum, we can see that period of a pendulum does not depend on the mass suspended. Hence, two pendulums having the same length but different masses will have the same period. Also, two pendulums with different lengths will have different time periods; the pendulum with the longer string will have the longer time period.