Question

The length of pendulum 1 is four times the length of pendulum 2. How does the period of pendulum 1 compare to the period of pendulum 2?

• A. The period of pendulum 1 is four times as much as the period of pendulum 2.
• B. The period of pendulum 1 is sixteen times as much as the period of pendulum 2.
• C. The period of pendulum 1 is twice as much as the period of pendulum 2.
• D. The period of pendulum 1 is one-half as much as the period of pendulum 2.
• E. We cannot determine the comparisons of the periods of the pendulums without knowing the masses of the pendulums.

Answer 1

Answer: (C)

The period of pendulum 1 is twice as much as the period of pendulum 2.

Time period $T$ of a pendulum of length $l$ is given by ,

$T=2\pi \sqrt{l/g}$ ,

for pendulum 1 ,

$T_1=2\pi \sqrt{l_1/g}$

for pendulum 2 ,

$T_2=2\pi \sqrt{l_2/g}$ , ..........................1

given $l_1=4l_2$ ,

therefore , $T_1=2\pi \sqrt{4l_2/g}$, ............................2

dividing 2 by 1 , we get

$T_1/T_2=\sqrt{4}=2$ ,

or $T_1=2T_2$

so option C is correct .