Question

There are two bodies of masses $100\text{kg}$ and $10000\text{kg}$ seperated by a distance $1\text{m}$. At what distance from the smaller body, the intensity of gravitational field will be zero.

• A. $\frac{1}{9}\text{m}$
• B. $\frac{1}{10}\text{m}$
• C. $\frac{1}{11}\text{m}$
• D. $\frac{10}{11}\text{m}$

Answer 1

The correct option is C $\frac{1}{11}\text{m}$

Let $\text{P}$ be the point at distance $x$ from the mass $100\text{kg}$ where net gravitational field intensity, $E_{net}=0$. So,

$E_1=E_2...\left(1\right)$

In the figure, $E_1$ and $E_2$ are the field intensities at point $\text{P}$ due to masses $100\text{kg}$ and $10000\text{kg}$ respectively.

Substituting the values in equation we get,

$\Rightarrow \frac{G\times 100}{x^2}$ = $\frac{G\times 10000}{(1-x{)}^2}$

$\Rightarrow {\left(\frac{1-x}{x}\right)}^2=(10{)}^2$

$\Rightarrow 1-x=\pm 10x$

$\Rightarrow x=\frac{1}{11}\text{m}$

Hence, Option (c) is the correct answer.

$\text{Key point:}$ The equilibrium is obtained at a point that is closer to the lighter body.