Question

To double the period of oscillation of a simple pendulum with small swings

1.

Its length should be quadrupled

2.

The mass of the bob should be quadrupled

3.

Its length should be doubled

4. The mass of the bob should be doubled 

Answer 1

Correct Answer - Option 1 :

Its length should be quadrupled

Concept:

The period of oscillation of a simple pendulum is given by the following formula:

\({\rm{T = 2\pi }}\sqrt {\frac{{\rm{L}}}{{\rm{g}}}} \)

Where

L = length of the pendulum

g = acceleration due to gravity

Calculation:

Now, if T’ = 2T

\({\rm{2\pi }}\sqrt {\frac{{{\rm{L'}}}}{{\rm{g}}}} {\rm{ = 2 \times 2\pi }}\sqrt {\frac{{\rm{L}}}{{\rm{g}}}} \)

L’ = 4L

Thus, in order to double the period of oscillation the length of pendulum should be quadrupled.