Question

There are two bodies of masses 100 kg and 10000 kg separated by a distance 1m. At what distance from the smaller body, intensity of gravitational field will be zero?

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

Answer 1

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

As shown in figure let a point $O$ beat a distance $x_n$ from $100kg$ and intensity of gravitational field at this point due to given two masses is zero. We are interested in intensity of gravitational field at the point $O$ due to given two masses $100kg$ and $1000kg$. Hence we need to find the gravitational forces $F_1$ and $F_2$ which are acting between unit mass placed at $O$ and each of two gives masses.

We assume intensity at $O$ is zero so $F_1=F_2$

Hence we have

$h\frac{100}{x^2}=\frac{h10000}{{(1-x)}^2}⟶\left(1\right)$

By simplying eq $\left(1\right)$ we get

${\left(\frac{x}{1-x}\right)}^2=\frac{1}{100}$ or $x=\frac{1}{11}R$.