Chapter 12, Problem 43A

What happens to the rotational inertia of a simple pendulum when both the mass of the bob and the length of the pendulum are doubled?

To determine

Resulting rotational inertia.

Answer to Problem 43A

The resulting rotational inertia is eight times the original one that is $I\text{'}=8I$

Explanation of Solution

Given:

Mass of the bob is doubled.

Length of the pendulum is also doubled.

Formula Used:

The rotational inertia of simple pendulum is given as,

  $I=m{L}^2$

Where, $m$ is the mass of bob and $L$ is length of pendulum.

Calculation:

New mass of bob is, $m\text{'}=2m$ and

New length of pendulum is, $L\text{'}=2L$

So resulting rotational inertia is,

  $\begin{array}{l}I\text{'}=m\text{'}L{\text{'}}^2\\ =2m\times {\left(2L\right)}^2\\ =8m{L}^2\\ \Rightarrow I\text{'}=8I\end{array}$

Conclusion:

Therefore, the resulting rotational inertia of simple pendulum is eight times the original one that is

  $I\text{'}=8I$