Two heavy spheres each of mass `100kg` and radius `0.1m` are placed `1m` apart on a horizontal table. What is the gravitationl field and potential at the mid point of the line joining their centres. The gravitational potential difference between the surface of a planet and a point `20m` above it is `16J//kg`. Calculate the workdone in moving a `2kg` mass by `8m` on a slope of `60^@` from the horizontal.

Explanation

Gravitational field at the mid point of the line joining their centres is given by `vec(E)=(GM)/((r//2)^(2))(vec(-r))+(GM)/((r//2)^(2))(vec(r))=bar(0)`
Gravitational potential at the mid point of the line joining their centres is given by
`V=(-GM)/((r//2))+(-GM)/((r//2))=(-4GM)/r`
`=-(4xx6.67xx10^(-11)xx100)/1=-2.7xx10^(-8)J//kg`