Question

The time period of a simple pendulum of length $l$ is $T$. If its length is increased to $4l$, its new time period will be

• A. $2T$
• B. $4T$
• C. $T/2$
• D. $T$

Hint:

Remember that for a simple pendulum, doubling the length results in a doubling of the time period due to the square root relationship in the formula.

Answer 1

The Correct Option is A

Step 1: Recall the pendulum period.
A simple pendulum of length $l$ has period \[ T = 2\pi\sqrt{\frac{l}{g}} \] The period depends on the square root of the length.

Step 2: Note the new length.
The length is made four times bigger, so the new length is $4l$.

Step 3: Write the new period.
Put $4l$ in place of $l$. \[ T_{new} = 2\pi\sqrt{\frac{4l}{g}} \]

Step 4: Pull out the four.
The square root of $4$ is $2$, so it can come out. \[ T_{new} = 2\pi\cdot 2\sqrt{\frac{l}{g}} \]

Step 5: Compare with the old period.
Since $T = 2\pi\sqrt{\dfrac{l}{g}}$, we see \[ T_{new} = 2\,T \]

Step 6: State the answer.
Making the length four times longer makes the swing twice as slow. \[ \boxed{T_{new} = 2T} \]