The distance between the centers of the moon | vedclass

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

Question

(D) Let $M_E$ be the mass of the earth and $M_M$ be the mass of the moon. Given $M_E = 81 M_M$ and the distance between them is $D$.Let the point wher

Vedclass · Accepted Answer

$\frac{9D}{10}$

Vedclass · Answer

(D) Let $M_E$ be the mass of the earth and $M_M$ be the mass of the moon. Given $M_E = 81 M_M$ and the distance between them is $D$.Let the point where the gravitational field is zero be at a distance $x$ from the center of the earth.At this point,the gravitational field due to the earth must be equal in magnitude to the gravitational field due to the moon.$\frac{G M_E}{x^2} = \frac{G M_M}{(D - x)^2}$Substituting $M_E = 81 M_M$:$\frac{81 M_M}{x^2} = \frac{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$$9D - 9x = x$$10x = 9D$$x = \frac{9D}{10}$

The distance between the centers of the moon and the earth is $D$. If the mass of the earth is $81$ times that of the moon,at what distance from the center of the earth will the gravitational field be zero?

Similar Questions

What is the relationship between gravitational field intensity $(I)$ and gravitational potential $(V)$ at a point?

$A$ thin rod of length $L$ is bent in the form of a circle. Its mass is $M$. What force will act on a mass $m$ placed at the centre of this circle? $(G = \text{universal gravitational constant})$

What is the gravitational field intensity at any point inside a uniform spherical shell?

For the given hemispherical shell,the direction of the gravitational intensity at an arbitrary point $P$ on its rim is indicated by which arrow?

Vedclass Test Series

Exam Paper Generator

Online Exam Module