If two bodies od masses 1kg and 4kg are released from the heights where gravitational force on them is equal, then find the height of the heavier body if the lighter body is dropped from a height of 1 km. Take radius of earth as 6400 km.

Explanation

(i) (1.) Find the height from where the lighter body of mass 1kg is dropped from the given data. Find the gravitational force of attraction on the lighter body when it is at given height (1 km), using the formula, `F = (GMm)/((R + h)^(2))`
(2.) If a body of mass 4 kg is to experience the same gravitational force of attraction as that of a body of 1 kg mass, find the required conditions.
Here, the force F is proportional to mass and inversely proportional to the `(R + h)^(2)`.
When mass is increased from 1 kg to 4 kg, then will the distance also increase?
Now, take the height of 4 kg mass as 'x'.
Then,`" "(GMm)/((R + h)^(2)) = (GM(4m))/((R + x)^(2))`
Find the value of 'x' by appropriate substitutions in equation (2).
(ii) 6402 km