Question

Two objects attract each other with a gravitational force of magnitude 0.96 ✕ 10-8 N when...

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)

Homework Answers

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

Hope this helps you..
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