two identical objects exert a gravitational force of -0.016 N onto each other when they are 0.25 cm apart.
What is the mass of each object?
3871 kg
24.0 kg
38.7 kg
1499 kg
C) 38.7 kg
To find the mass of each object, we can use Newton's law of universal gravitation which states that the gravitational force between two objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.
The formula for gravitational force is given as:
F = G * (m1 * m2) / r^2
Where:
F is the gravitational force,
G is the gravitational constant (approximately 6.673 × 10^-11 N m^2 / kg^2),
m1 and m2 are the masses of the objects, and
r is the distance between their centers.
Given:
F = -0.016 N,
r = 0.25 cm = 0.0025 m,
G = 6.673 × 10^-11 N m^2 / kg^2.
Here, we need to solve for m1 and m2. Since the objects are identical, their masses will be the same.
Rearranging the formula, we get:
(m^2) = (F * r^2) / G
Now, substitute the given values:
(m^2) = (-0.016 N * (0.0025 m)^2) / (6.673 × 10^-11 N m^2 / kg^2)
m^2 = -0.016 N * (0.0025 m)^2 * (1 / (6.673 × 10^-11 N m^2 / kg^2))
m^2 = -0.016 N * 0.00000625 m^2 * (1 / (6.673 × 10^-11 N m^2 / kg^2))
m^2 = -0.010^-7 kg
Taking the square root of both sides, we get:
m ≈ ±0.0003 kg
Since mass cannot be negative, we take the positive value:
m ≈ 0.0003 kg
Therefore, the mass of each object is approximately 0.0003 kg.
None of the given answer options match this value, so there may be an error in the calculations or the provided choices.
Use Newton's law and solve for m:
Gm^2/0.0025^2 = 0.016