Chapter 11, Problem 31P

(a)

To determine

To Find: The period of simple pendulum.

Answer to Problem 31P

The period of a pendulum on Earth is $1.8\text{ s}$ .

Explanation of Solution

Given:

Length of pendulum $l=80\text{ cm }=0.80\text{ m}$

Formula used:

The period of a pendulum is determined by the following formula,

  $\text{Period }T=2\pi \times \sqrt{\frac{l}{g}}$

Here,

  $T$ is time period of pendulum,

  $l$ is the length of pendulum,

  $g$ is the acceleration due to gravity.

Calculation:

Substitute the given values in the above formula,

  $T=2\pi \times \sqrt{\frac{0.80}{9.8}}=1.8\text{ s}$

Conclusion:

Thus, the period of a pendulum on Earth is $1.8\text{ s}$ .

(b)

To determine

To Find: The period of simple pendulum.

Answer to Problem 31P

The period of a pendulum when it is in freely falling elevator is $\text{0 }$ .

Explanation of Solution

Given:

Consider the elevator is in freely falling condition.

Formula used:

The period of a pendulum is determined by the following formula,

  $\text{Period }T=2\pi \times \sqrt{\frac{l}{g}}$

Here,

  $T$ is time period of pendulum,

  $l$ is the length of pendulum,

  $g$ is the acceleration due to gravity.

Calculation:

If, pendulum is in free fall elevator, there is no tension in string. There is no restoring force to cause the oscillation and hence there is no tension.

Conclusion:

Thus, the period of a pendulum when it is in freely falling elevator is $0$ .