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