Two solid spheres of radius 10 cm and masses 800 kg and 600 kg, are at a distance 0.25 m apart. Calculate distance 0.20 m from the 800 kg sphere and 0.1 m from the 600 kg sphere and does not lie on the line joining their centres. Given, `G = 6.6 xx 10^(-11) N-m^(2) kg^(-2)`.

Explanation

Let `E_(A)` be the gravitational field intensity at P due to 800 kg sphere at A

Then, `E_(A)=G(800)/((0.2)^(2))=2xx10^(4)` along PA
Let `E_(B)` be the gravitational field intensity at P due to 600 kg sphere at B
Then, `E_(B)=G(600)/((0.15)^(2)) "along" PB=(8000 G)/(3)` along PB
The angle between `E_(A) adn E_(B)` is `90^(@)" "[because AB^(2)=AP^(2)+BP^(2)]`
If E be the magnitude of the resultant intensity, then
`E=sqrt(E_(A)^(2)+E_(B)^(2))`
`=sqrt((2xx10^(4)G)^(2)+((80000G)/(3))^(2))`
`=Gsqrt(4xx10^(8)+(64)/(9)xx10^(8))`
`=6.67 xx10^(-11)xx2xx10^(4)sqrt(1+(16)/(9))`
`=6.67xx2xx(5)/(3)xx10^(-7)"N kg"^(-1)`
`rArr E=2.22 xx10^(-6)"N kg"^(-1)`.