Question

What is the magnitude of the gravitational force between two objects of 100 kg and 250 kg each separated by a 1.5 m distance? Use G = 6.67⋅10^-11 N⋅m²/kg².  

Answer 1

We know, gravitational force is defined as the the attractive force F acting between two bodies such that it varies directly with the product of masses of two bodies(say m1 and m2) and inversely with the square of distance(r) between them. Mathematically, we can write;

F = G M_{​​​​​​1}*M_{​​​​​​2}/ r^​​​2 ......eqn 1

Where G is the universal gravitational constant having value= 6.67*10^-11N m^{​​​​​​2}​​​ kg^{​​​​^(-2)}

Given, M^{​​​​​​}_{​​​​​​​​​1} = 100 kg

M_{​​​​​​2} = 250 kg

And r = 1.5 m

Hence, using these values in eqn 1, we get

F = 6.67*10^-11* 100*250/(1.5)²

= 166750*10^-11/2.25

= 74111.11*10^-11

Multiplying and dividing by 10⁴, we get

F = 74111.11*10^-11*10⁴/10⁴

F = 7.411*10^-7 N.... Required gravitational force acting between the two bodies of masses 100 kg and 250 kg respectively.