Chapter 11, Problem 82GP

(a)

To determine

The length of second pendulum.

Answer to Problem 82GP

  $0.9932\text{m}$

Explanation of Solution

Given Information:

Time period of pendulum, $T=2\text{s}$

Acceleration due to gravity, g = $9.793{\text{m/s}}^{\text{2}}$

Formula used:

Period of pendulum is

  $T=2\pi \sqrt{\frac{l}{g}}-(1)$

Here, l is the length of the pendulum.

Calculation: From equation 1

  $\begin{array}{l}2=2\pi \sqrt{\frac{l}{9.793}}\\ 1=3.14\sqrt{\frac{l}{9.793}}\\ \sqrt{l}=\frac{1}{1.00341}\\ l=0.9932\text{m}\end{array}$

Conclusion:

Thus, the length of the pendulum is $0.9932\text{m}$ .

(b)

To determine

The required increase in the length of the pendulum.

Answer to Problem 82GP

  $2.24\text{mm}$

Explanation of Solution

Given Information: Time period of pendulum, T = 2 s

Acceleration due to gravity, g = $9.809{\text{m/s}}^{\text{2}}$

Formula used: Period of pendulum is

  $T=2\pi \sqrt{\frac{l}{g}}-(1)$

Here, l is the length of the pendulum.

Calculation: From equation 1

  $\begin{array}{l}2=2\pi \sqrt{\frac{l}{9.809}}\\ 1=3.14\sqrt{\frac{l}{9.809}}\\ \sqrt{l}=\frac{1}{1.00258}\\ l=0.9948\\ \Delta l=0.9948-0.9932\\ \Delta l=0.0016\text{m}\\ \Delta l=\text{1}\text{.6 mm}\end{array}$

Conclusion:

The pendulum must be lengthened by $\text{1}\text{.6 mm}$ .

(c)

To determine

The length of second pendulum on the moon.

Answer to Problem 82GP

The length of second pendulum on the moon is $0.1643\text{m}$ .

Explanation of Solution

Given Information: Time period of pendulum T = 2 s

Acceleration due to gravity, $g=\text{1}\text{.62}{\text{m/s}}^{\text{2}}$

Formula used:

Period of pendulum is

  $T=2\pi \sqrt{\frac{l}{g}}-(1)$

Here, l is the length of the pendulum.

Calculation: From equation 1

  $\begin{array}{l}2=2\pi \sqrt{\frac{l}{1.62}}\\ 1={(}^{\pi }\frac{l}{1.62}\\ l=0.1643\text{m}\end{array}$

Conclusion:

Thus, the length of the pendulum is $0.1643\text{m}$ .