The distance between the centre of the moon a | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Let a unit mass $m$ be placed at a distance $x$ from the centre of the earth,where the net gravitational force is zero.At this point,the gravitati

Vedclass · Accepted Answer

$\frac{9 D}{10}$

Vedclass · Answer

(D) Let a unit mass $m$ be placed at a distance $x$ from the centre of the earth,where the net gravitational force is zero.At this point,the gravitational pull from the earth must be equal in magnitude to the gravitational pull from the moon.$\frac{G m M_e}{x^2} = \frac{G m M_m}{(D-x)^2}$ ... $(i)$where $M_e$ is the mass of the earth and $M_m$ is the mass of the moon.Given that $M_e = 81 M_m$.Substituting this into equation $(i)$:$\frac{G m (81 M_m)}{x^2} = \frac{G m M_m}{(D-x)^2}$$\frac{81}{x^2} = \frac{1}{(D-x)^2}$Taking the square root on both sides:$\frac{9}{x} = \frac{1}{D-x}$$9(D - x) = x$$9D - 9x = x$$9D = 10x$$x = \frac{9D}{10}$Thus,the gravitational force is zero at a distance of $\frac{9D}{10}$ from the centre of the earth.

The distance between the centre of the moon and the earth is $D$ and the mass of the earth is $81$ times the mass of the moon. At what distance from the centre of the earth will the net gravitational force on an object be zero?

Similar Questions

According to Newton's law of gravitation,both the Earth and an apple exert equal forces on each other. Why does the apple fall towards the Earth,but the Earth does not move towards the apple?

We can shield a charge from electric fields by putting it inside a hollow conductor. Can we shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?

$A$ mass $M$ is divided into two parts $xM$ and $(1 - x)M$. For a given separation,the value of $x$ for which the gravitational attraction between the two pieces becomes maximum is

An astronaut of mass $m$ is working on a satellite orbiting the Earth at a distance $h$ from the Earth's surface. The radius of the Earth is $R$,while its mass is $M$. The gravitational pull $F_G$ on the astronaut is

Two identical solid copper spheres of radius $R$ are placed in contact with each other. The gravitational attraction between them is proportional to

Vedclass Test Series

Exam Paper Generator

Online Exam Module