Question

Two objects attract each other with a gravitational force of magnitude 0.96 ✕ 10^-8 N when separated by 19.3 cm. If the total mass of the two objects is 5.06 kg, what is the mass of each?
kg (heavier mass)
kg (lighter mass)

Answer 1

Sol:

Given

Fg= 0.96*10^-8 N
Distance(r)=19.3 cm =0.193 m
Total mass of the two objects
(m1+m2)=5.06 kg

We have

F(grav) = G m1 m2/r^2 = 0.96*10^-8

G m1 m2/r^2 = 0.96*10^-8
m1 m2 = 0.96*10^-8*(r)^2 / G
m1 m2 = 0.96*10^-8*(0.193)^2 / 6.67*10^-11
=0.00536*10^3
=5.36 kg^2
Now

givem m1+m2 = 5.06 kg

(m1 - m2)^2 = (m1+m2)^2 - 4m1 m2
(m1 - m2)^2 = 25.6036 - 4*5.36
= 4.1636
m1 - m2 = 2.040
m1 + m2 = 5.06
Adding the two equations
2m1 = 7.1

m1 =3.55 kg
So
m2 = 1.51 kg

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