Question

Two objects attract each other with a gravitational force of magnitude 0.98 x 10-8 N when separated by 19.5 cm. If the total mass of the two objects is 5.09 kg, what is the mass of each? kg (heavier mass) kg (lighter mass)

Answer 1

M = 3.485 kg

m = 1.605 kg

Step-by-step explanation:

F = 0.98 x 10^-8 N

r = 19.5 cm = 0.195 m

M + m = 5.09 kg ...... (1)

By use of Newton's gravitational law

F = G m1 m2 / r^2

0.98 x 10^-8 = 6.67 x 10^-11 x M x m / (0.195)^2

M x m = 5.59

`M - m = \sqrt{(M + m)^(2)-4 M m}`

`M - m = \sqrt{(5.09)^(2)-4 * 5.59}`

M - m = 1.88 .........(2)

By solving the equation (1) and equation (20, we get

M = 3.485 kg

m = 1.605 kg