Question

a rocket is fired from the Earth surface to the moon surface the distance between the centre of earth and the moon is a in the mass of the earth is 81 times the mass of the Moon the gravitational force on the rocket will be zero when its distance from the moon is​

Answer 1

Answer:

A gravitational force of the moon will be zero when its distance is  $\frac{r}{10}$.

Solution:

According to Newton's law,

The force of attraction is $=\frac{G M m}{R^{2}}$

G = universal gravitational constant,

$M_e$ = 81 times of mass of the moon.

Let the rocket be distance x from the moon when the gravitational force on it is zero. Its distance from the earth  $=r-x$. Gravitational force on rocket due to earth is

$F_{e}=\frac{G m M_{e}}{(r-x)^{2}}$

Where, m = mass of the rocket

$F_{m}=\frac{G m M_{m}}{x^{2}}$

By equating the two equation, we get

$\begin{array}{c}{\frac{G m M_{c}}{(r-x)^{2}}=\frac{G m M_{m}}{x^{2}}} \\ {\frac{r-x}{x}=\sqrt{\frac{M_{e}}{M_{m}}}=\sqrt{81}=9}\end{array}$

$\begin{array}{l}{r-x=9 x} \\ {9 x+x=r=10 x} \\ {x=\frac{r}{10}}\end{array}$

Where, r is the distance between the moon and the earth.

Answer 2

Answer:

A gravitational force of the moon will be zero when its distance is  .

Solution:

According to Newton's law,

The force of attraction is  

G = universal gravitational constant,

= 81 times of mass of the moon.

Let the rocket be distance x from the moon when the gravitational force on it is zero. Its distance from the earth  . Gravitational force on rocket due to earth is

Where, m = mass of the rocket

By equating the two equation, we get

Where, r is the distance between the moon and the earth.

Explanation: