Correct Option
The motion of a swing can be approximated as a simple pendulum. The time period (T) of a simple pendulum is given by the formula: T = 2π√(L/g), where L is the effective length of the pendulum from the point of suspension to the center of mass of the oscillating system, and g is the acceleration due to gravity.
When the girl is in a sitting position, her center of mass is at a certain distance from the point of suspension. When she stands up, her center of mass shifts upwards, moving closer to the point of suspension. This action effectively reduces the effective length (L) of the pendulum. Since the time period T is directly proportional to the square root of L, a decrease in L results in a shorter time period. Therefore, the swing will oscillate faster, and its period will be shorter.
Incorrect Options
Option (2) is incorrect because a longer period would imply an increase in the effective length (L), which is contrary to what happens when the girl stands up and her center of mass moves closer to the suspension point.
Option (3) is incorrect because the period of the swing depends on the effective length to the center of mass of the system, not merely the girl's overall height. The change in the position of the center of mass is the crucial factor determining the change in the period.
Option (4) is incorrect because the period of the swing does change. The change in the girl's position alters the effective length (L) of the pendulum system, which in turn changes the time period T.