To calculate the mass of two identical objects based on the force and distance between their centers, you need to use Newton's law of universal gravitation. The formula for gravitational force between two objects is:
F = (G * m1 * m2) / r^2
Where: F is the gravitational force between the objects, G is the gravitational constant (approximately 6.674 × 10^-11 N m^2/kg^2), m1 and m2 are the masses of the objects, and r is the distance between their centers.
In your case, the force (F) is given as 6.67 × 10^-13 (I assume you meant Newtons), and the distance (r) between the object centers is 10 cm, which is equal to 0.1 meters. We can plug these values into the formula and solve for the masses (m1 and m2):
6.67 × 10^-13 = (6.674 × 10^-11 * m1 * m2) / (0.1)^2
Simplifying the equation:
6.67 × 10^-13 = (6.674 × 10^-11 * m1 * m2) / 0.01
Rearranging the equation:
m1 * m2 = (6.67 × 10^-13 * 0.01) / (6.674 × 10^-11)
m1 * m2 = 0.00667 / 0.06674
m1 * m2 = 0.1000
Since the two objects are identical, let's assume their masses are the same, so we can express them as m1 = m2 = m. Substituting this into the equation:
m * m = 0.1000
Taking the square root of both sides:
m = √(0.1000)
m ≈ 0.316 kg
Therefore, the mass of each identical object is approximately 0.316 kg.