AIIMS 2000 Physics Gravitational Field Strength MCQ Question

To find the point where the gravitational fields due to the Earth and the Moon cancel each other, we can use the formula for gravitational field strength, which is given by $E = \frac{G M}{r^2}$, where $G$ is the gravitational constant, $M$ is the mass of the object, and $r$ is the distance from the object.

Let the distance from the Moon to the point where the fields cancel be $x$. Therefore, the distance from the Earth to this point will be $60R - x$.

The mass of the Moon is $\frac{M}{81}$ and the mass of the Earth is $M$. Setting the gravitational fields equal gives us: $\frac{G M}{(60R - x)^2} = \frac{G \frac{M}{81}}{x^2}$

We can cancel $G$ and $M$ from both sides: $\frac{1}{(60R - x)^2} = \frac{1/81}{x^2}$

Cross-multiplying leads to: $x^2 = \frac{(60R - x)^2}{81}$

Taking the square root of both sides: $9x = 60R - x$ $10x = 60R$ $x = 6R$

Thus, the distance from the Moon where the gravitational fields cancel is $6R$.

The other options are incorrect because they do not satisfy the gravitational field balance condition derived above.