Calculate the distance between the center of the earth and the center of the moon at which the gravitational force exerted by the earth on the object is equal in magnitude to the force exerted by the moon on the object

Solution:

Step wise solution

Let r1 be the distance from the Earth to the point where

the gravitational accelerations are the same and let r2 be the distance

from the Moon to that point.

Then, r1+ r2 = r12 = 383,000 km.

Let Re be the radius of earth

and let Rm be the radius of moon

Let, ge be the gravity of earth

and let gm be the gravity of moon

The fact that the gravitational attractions by the Earth and the Moon

at this point are equal leads to the equation

gE(Re/r1)=gM(Rm/r2)

9.8(6380/r1)=1.62(1738/r12-r1)              

(here, Re=6380, gE=9.8m/s^2,  gM=1.62m/s^2 and r12=383,000 km

9.8*6380/(1.62*1738)=r1/(383000-r1)

therefore,

r1=344,770 km

Hope this answer wil help you

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