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

Hope this helps you..

Please VOTE my answer

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