Question

Derivation for F =Gm₁m₂/r² and some related problems to this derivation ?

Answer 1

Suppose two bodies of masses m₁ and m₂ are at distance of r meters from each other.

now,
as the force between the object is directly proportional to the prodeuct of their masses then,

force ∝ m₁ × m₂------- (i)

and by kepler's third law of motion it was derived that
force between two objects is inversely proportional to the square of their masses so,

force ∝ r² ---------(ii)


combine (i) and (ii)
you'll end up with

force ∝m₁m₂/r²

now, to remove the sign of proportionality you must add a constant on the RHS and here we are going to use G whose value is 6.67 × 10 ^(-11)


multiply with this constant and you'll get

Force = Gm₁m₂/r²




Questions :

1. what would be the weight of a 1 kg bodylyung on the surface of earth?
take G as 6.7 × 10^(-11)


2. If the distance between two masses is increased by a factor of 5, by what factor would the mass of one of themhave to be altered to maintain the gravitational force?


3. suppose a planet exists whose mass a d radius both are half of those of earth. calculate the value of g on it's surface.

4. two bodies P and Q having masses 2kg and 4 kg respectively are seperated by 2m. where should another mass R, weighting 1 kg be kept , so thatthe gravitational force on R due to P and Q is 0?

5. If you weight 60N on earth, how far must you go above the surface of the earth so that you weight 30kg?