Chapter 7, Problem 74A

a.

To determine

Value of $g$ for the given condition.

Answer to Problem 74A

The new value of $g$ is $29.4\text{N/kg}$

Explanation of Solution

Given:

Mass of earth is triple its actual value.

Radius is same as the actual.

Formula Used:

The gravitational field due to Earth is,

  $g=\frac{G{m}_E}{{\left(r_E\right)}^2}$

Calculation:

New mass = $3m_E$ and radius = $r_E$

The gravitational field will be,

  $\begin{array}{c}g\text{'}=\frac{G\left(3m_E\right)}{{\left(r_E\right)}^2}=3g\\ =3\times 9.8\text{N/kg}\\ =29.4\text{N/kg}\end{array}$

Conclusion:

Therefore, the value of gravitational field is $29.4\text{N/kg}$

b.

To determine

Value of $g$ for the given condition.

Answer to Problem 74A

The new value of $g$ is $1.089\text{N/kg}$

Explanation of Solution

Given:

Earth’s radius is tripled and mass remains the same.

Formula Used:

The gravitational field due to Earth is,

  $g=\frac{G{m}_E}{{\left(r_E\right)}^2}$

Calculation:

New mass = $m_E$ and radius = $3r_E$

The gravitational field will be,

  $\begin{array}{c}g\text{'}=\frac{G{m}_E}{{\left(3r_E\right)}^2}=\frac{g}{9}\\ =\frac{9.8}{9}\text{N/kg}\\ =1.089\text{N/kg}\end{array}$

Conclusion:

Therefore, the value of gravitational field is $1.089\text{N/kg}$

c.

To determine

Value of $g$ for the given condition.

Answer to Problem 74A

The new value of $g$ is

  $4.9\text{N/kg}$

Explanation of Solution

Given:

Earth’s radius is doubled and mass is also doubled.

Formula Used:

The gravitational field due to Earth is,

  $g=\frac{G{m}_E}{{\left(r_E\right)}^2}$

Calculation:

New mass = $2m_E$ and radius = $2r_E$

The gravitational field will be,

  $\begin{array}{c}g\text{'}=\frac{G\left(2m_E\right)}{{\left(2r_E\right)}^2}\\ =\frac{g}{2}\\ =\frac{9.8}{2}\text{N/kg}\\ =4.9\text{N/kg}\end{array}$

Conclusion:

Therefore, the value of gravitational field is $4.9\text{N/kg}$