Question 357: 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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