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If the distance between centres of earth and moon is D and mass of earth is 81 times that of moon. At what distance from the centre of earth, the gravitational field will be zero? Pls provide proper solution.

If the distance between centres of earth and moon is D and mass of earth is 81 times that of moon. At what distance from the centre of earth, the gravitational field will be zero? Pls provide proper solution.

Grade:11

6 Answers

Vikas TU
14149 Points
7 years ago
The net gravitaional force due to both would be zero then after.
Hence
gravity Earth + gravity moon  = 0
Gm/(x^2)+ GM/(D-x)^2 = 0
Aand given M = 81m
We get,
Gm/(x^2) + 81Gm/(D-x)^2
1/x = 9/(D-x)
9x = D-x
10x = D
x = D/10
10x = D
x = D/10
Rochita
11 Points
6 years ago
The net gravitation force on both will be zero.So, F1=F2 Gm/(D-x)^2 = G81m/x^2Now we get, x/D-x = 9 x= 9D-9x 10x =9D x= 9D/10
prakash
13 Points
5 years ago
Mass of Earth is 81times of moon 
So here is the equation
GM(Mass of Earth )/x =Gm(Mass of moon )/(D-x) me G×81m /x = GM /(D-x)
After solving the equation 
You will get,
9D/10 (answer)
Nancy bachwani
13 Points
5 years ago
The gravitation will be zero if F1+F2=0 or F1=F2
Given that the mass of earth is 81 times the mass of moon 
Therefore we have :
GM/(D-x)^2=G.81M/x^2
By solving we get 9D/10 as ans
Thank you
 
Shweta
13 Points
4 years ago
Force will be zero at the x distance from the earth and (D-x) distance from the moon .So by given information we can write the following equation :
:
GMm/x^2=GMm/81×(D-x)^2
Solving this expression we get ,
x=9D/10
Yash Chourasiya
askIITians Faculty 256 Points
3 years ago
Dear Student

Lets assume there is a particle of massmfromxdistance away from earth. assuming gravitational force onmis zero so :-.
Force balance
643-79_Untitled.png

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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