The length of a simple pendulum is decreased by $21\%.$ The percentage change in its time period is :
- $11\%$ decrease
- $51\%$ increase
- $21\%$ decrease
- $31\%$ decrease
The time period of a simple pendulum is directly proportional to the square root of its length. If the length is decreased by 21%, the new length is 79% of the original length, making the new time period proportional to sqrt(0.79), which is approximately 0.89, representing an 11% decrease.
The time period of a simple pendulum is given by the formula T = 2*pi*sqrt(L/g), meaning time is proportional to the square root of length. A 21 percent decrease in length means the new length is 0.79 times the original, making the new time period sqrt(0.79) times the original. Calculating sqrt(0.79) gives approximately 0.889, which represents an 11.1 percent decrease in the time period. Therefore, the percentage change is an 11 percent decrease.