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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.

Priyanka lalwani , 7 Years ago

Grade 11

6 Answers

Vikas TU

Last Activity: 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

Approved

Rochita

Last Activity: 7 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

Last Activity: 6 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

Last Activity: 6 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

Last Activity: 5 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

Last Activity: 4 Years ago

Dear Student

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

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