Question

Two objects attract each other with a gravitational force of magnitude 9.30 10-9 N when separated by 20.0 cm. If the total mass of the objects is 5.08 kg, what is the mass of each? heavier mass? lighter mass?

Answer 1

Write the formula for Gravitational force of attraction -
F = G m₁m₂/r²

Where,
G = 6.67 x10^-11 m³/kgs²
m₁ and m₂ are the masses of the two objects in kg
r is the distance in meters between their centers

Now, consider the two masses as x and y -
F = (6.67e-11)(x)(y) / (0.20)² = 9.30x10^-9

=> (6.67e-11)(x)(y) = 3.72 x 10^-10

=> xy = 5.58

Again, x+y = 5.08
x = 5.08–y

Substituting in the above -
xy = 5.58
(5.08–y)y = 5.58
y² – 5.08y + 5.58 = 0

=> y = [5.08 + sqrt(5.08^2 - 4*5.58)]/2 = [5.08 + 1.87]/2 = 3.47 kg
Second value of y = [5.08 - sqrt(5.08^2 - 4*5.58)]/2 = [5.08 - 1.87]/2 = 1.61 kg

So, the heavier mass = 3.47 kg and lighter mass = 1.61 kg.