Question

Assertion: When a girl sitting on a swing stands up, the periodic time of the swing will increase.
Reason: In standing position of a girl, the effective length of the swing will decrease.
A. both Assertion and Reason are true and Reason is the correct explanation of the Assertion.
B. both Assertion and Reason are true but Reason is not a correct explanation of the Assertion.
C. Assertion is tru2 but the Reason is false.
D. both Assertion and Reason are false.

Answer 1

When a simple pendulum oscillates the time period of oscillation depends on the length of the suspension from the centre of gravity of the pendulum. Use this formula to explain the problem.

Formula used:
The time period of a simple pendulum is given by,
$T = 2\pi \sqrt {\dfrac{l}{g}}$
where $l$ is the distance from the centre of gravity of the bob to the suspension point and $g$ is the gravitational acceleration.

Complete step by step answer:
In the Assertion it is stated that a girl is sitting on a swing when she stands up, the periodic time of the swing will increase.Now, when the girl is sitting on the swing and swinging the centre of gravity of the girl is close to the ground meaning at a higher distance from the point of suspension. When the girl stands up the centre of gravity shifts to a higher level from the ground hence the effective length of the swing decreases. Now, from the formula of time period we know,
$T = 2\pi \sqrt {\dfrac{l}{g}}$
So, in this problem, ${l_1} > {l_2}$ .Hence, the time period of the swing will be, ${T_1} > {T_2}$.Hence, Reason is the correct explanation of the Assertion.

Hence,the correct answer is option A.

Note: The time period of a pendulum only depends on the effective length of the swing. To solve this type problem one can remember the formula for the time period and give the correct explanation. If not able to recall the expression from the equation of a simple pendulum use the expression of frequency of oscillation to find the time period.