Question

Choose the correct alternative:

The formula –G Mm(1/r₂– 1/r₁) is more/less accurate than the formula mg(r₂– r₁) for the difference of potential energy between two points r₂and r₁distance away from the centre of the earth.

Answer 1

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Gravitational potential energy of two points r₂ and r₁ distance away from the centre of the Earth is respectively given by:

`V(r_1) = -(GmM)/r_1`

`V(r_2) =-(GmM)/r_2`

∴ Different in potential energy , `V = V(r_2) - V(r_1) = -GmM(1/r_2 - 1/r_1)`

Hence this formula is more accurate than the formula `mg(r_2-r_1)`