Chapter 13, Problem 26A

Calculate the force of gravity between a newborn baby $\left(mass=4kg\right)$ and the planet Mars $\left(mass=6.4\times {10}^{23}kg\right)$, when Mars is at its position closest to Earth $\left(distance=8\times {10}^{10}m\right)$.

To determine

Force of gravity between a new-born baby and the planet Mars.

Answer to Problem 26A

Force of gravity $F=2.668\times {10}^{-8}\text{N}$

Explanation of Solution

Given:

The mass of baby is, $m_1=4\text{kg}$

The mass of the planet mars is, $m_2=6.4\times {10}^{23}\text{kg}$

Mars position closest to Earth, $r=8\times {10}^{10}\text{m}$

Formula Used:

From Newton’s law of gravitation,

  $F=\frac{G{m}_1{m}_2}{r^2}$

  $F$ is force of gravity, $G$ is gravitational constant, $m_1$ and $m_2$ are mass of two objects and $r$ is distance between the two objects.

Calculation:

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

On substituting the values in above relation, the force of gravity between new-born baby and the planet Mars, when Mars is closest to earth is

  $\begin{array}{l}F=\frac{\left(6.67\times {10}^{-11}{\text{N-m}}^2{\text{/kg}}^{\text{2}}\right)\times 4\times \left(6.4\times {10}^{23}\text{kg}\right)}{{\left(8\times {10}^{10}\text{m}\right)}^2}\\ =2.668\times {10}^{-8}\text{N}\end{array}$

Conclusion:

Therefore, the force of gravity between anew-born baby and the planet Mars, when Mars is closest to earth is $F=2.668\times {10}^{-8}\text{N}$ .