Chapter 7, Problem 62A

a.

To determine

The value of g on the dwarf planet Ceres.

Answer to Problem 62A

  $0.186{\text{m/s}}^2$

Explanation of Solution

Given:

The mass of the Ceres is $7\times {10}^{20}\text{}\text{kg}$ and its radius is $500\text{}\text{km}$ .

Formula used:

The value of g on any planet is given by,

  $g=\frac{GM}{R^2}$

Where, $G$ is the gravitational constant, $R$ is the radius of the planet, and $M$ is the mass of the planet.

Calculation:

The value of gravitational constant is,

  $G=6.67\times {10}^{-11}\text{N}{\text{.m}}^{\text{2}}{\text{/kg}}^{\text{2}}$

Then using the given values of mass and radius of the Ceres, the value of g will be,

  $\begin{array}{c}g=\frac{GM}{R^2}\\ =\frac{6.67\times {10}^{-11}\times 7\times {10}^{20}}{{\left(5\times {10}^5\text{}\text{m}\right)}^2}\\ =0.186{\text{m/s}}^2\end{array}$

Conclusion:

Thus, the value of g on the dwarf planet Ceres is $0.186{\text{m/s}}^2$ .

b.

To determine

The weight of 90-kg astronaut on Ceres.

Answer to Problem 62A

  $16.74\text{N}$

Explanation of Solution

Given:

The mass of the astronaut is 90-kg.

From part (a), the value of g on Ceres is $0.186{\text{m/s}}^2$ .

Formula used:

The weight of an object of mass m on the planet is given by,

  $W=mg$

Where, g is the gravitational field strength on the planet.

Calculation:

Using the given and calculated values, the weight of 90-kg astronaut on Ceres will be,

  $\begin{array}{c}W=mg\\ =90\times 0.186\\ =16.74\text{N}\end{array}$

Conclusion:

Thus, the of weight of a 90-kg astronaut on Ceres is $16.74\text{N}$ .