If the length of a simple pendulum is increased by 4% and the mass is decreased by 4%,the period is
A)not changed.
B)increased by 2%.
C)decreased by 4%.
D)increased by 4%.
E)decreased by 2%.

Question

Quizplus · Accepted Answer

The period of a simple pendulum is given by $T = 2\pi\sqrt{\frac{L}{g}}$, where $L$ is the length of the pendulum and $g$ is the acceleration due to gravity. The mass of the pendulum does not affect its period, so a decrease in mass has no effect on the period. An increase in length by 4% means the new length is $1.04L$. Substituting this into the formula gives $T_{new} = 2\pi\sqrt{\frac{1.04L}{g}} = T\sqrt{1.04}$. Since $\sqrt{1.04}$ is approximately 1.02, the period increases by approximately 2%.

If the Length of a Simple Pendulum Is Increased by 4