Question 373: Gravitation

Question

The mass of earth is 81 times the mass of the moon and the distance between their centres is $$R$$. The distance from the centre of the earth, where gravitational force will be zero is

Accepted Answer

Let $$x$$ be the distance from the centre of earth, where gravitational force is zero and $$m_0$$ be the point mass as shown below
Using Newton's law of gravitation,
Force between earth and point mass,
$$F_1=\frac{G 	imes 81 m 	imes m_0}{x^2} \quad 	ext{..... (i)}$$
and force between moon and point mass,
$$F_2=\frac{G 	imes m 	imes m_0}{(R-x)^2} \quad 	ext{.... (ii)}$$
According to the question,
$$\begin{array}{ll}
& F_1=F_2 \
\Rightarrow &  \frac{G 	imes 81 m 	imes m_0}{x^2}=\frac{F_2}{(R-x)^2} \
\Rightarrow & \frac{81}{x^2}=\frac{1}{(R-x)^2} \
\Rightarrow & \frac{9}{x}=\frac{1}{R-x} \
\Rightarrow \quad & x=\frac{9}{10} R
\end{array}$$

Answer

$$\frac{R}{4}$$

Answer

$$\frac{R}{2}$$

Answer

$$\frac{9 R}{10}$$

Answer

$$\frac{R}{81}$$

Gravitation

The mass of earth is 81 times the mass of the moon and the distance between their centres is $R$. The distance from the centre of the earth, where gravitational force will be zero is

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