Two spherical objects have equal masses and experience a gravitational force of 2.5 x 10^-9 N towards each other. Their centres are 0.50 m apart. Determine the value of each of their masses.*1 point1.3 kg3.1 kg13 kg31 kg
Question
Two spherical objects have equal masses and experience a gravitational force of 2.5 x 10^-9 N towards each other. Their centres are 0.50 m apart. Determine the value of each of their masses.*1 point1.3 kg3.1 kg13 kg31 kg
Solution
To solve this problem, we can use the formula for gravitational force:
F = G * (m1 * m2) / r^2
where: F is the gravitational force, G is the gravitational constant (6.674 * 10^-11 N(m/kg)^2), m1 and m2 are the masses of the two objects, and r is the distance between the centers of the two objects.
Given that the two objects have equal masses (m1 = m2 = m), the formula simplifies to:
F = G * m^2 / r^2
We can rearrange this formula to solve for m:
m = sqrt(F * r^2 / G)
Substituting the given values:
m = sqrt((2.5 * 10^-9 N) * (0.50 m)^2 / (6.674 * 10^-11 N(m/kg)^2))
m = sqrt((2.5 * 10^-9 N) * (0.25 m^2) / (6.674 * 10^-11 N(m/kg)^2))
m = sqrt((6.25 * 10^-10 N*m^2) / (6.674 * 10^-11 N(m/kg)^2))
m = sqrt(9.37 kg^2)
m = 3.06 kg
So, the closest answer is 3.1 kg.
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