Question

A heavier mass m1 and a lighter mass m2 are 20.5 cm apart and experience a gravitational force of attraction that is 8.50 10-9 N in magnitude. The two masses have a combined value of 5.80 kg. Determine the value of each individual mass.m1 = ____ kg

m2 = ____ kg

Answer 1

Answer:

m₁ = 4.65 Kg

m₂ = 1.15 Kg

Explanation:

given,

heavier mass be equal to m₁

lighter mass be equal to m₂

distance between the two objects = 20.5 cm = 0.205 m

force of attraction = 8.50 x 10⁻⁹ N

combine value of mass = 5.80

m₁ + m₂ = 5.80 Kg

using formula

$F = \dfrac{Gm_1m_2}{r^2}$

$8.5 \times 10^{-9} = \dfrac{6.67 \times 10^{-11}m_1( 5.8- m_1)}{0.205^2}$

$5.35 =m_1( 5.8- m_1)$

$m_1^2- m_1( 5.8) + 5.35 = 0$

on solving the above equation

m₁ = 4.65 Kg

now,

m₂ = 5.80 - 4.65

m₂ = 1.15 Kg