Two uniform spheres , each of mass M and radius R, touch one another. What is the magnitude of their gravitational force of attraction?
Isn't the distance the centers of mass are apart 2R?
Fg = G*m1*m2/r^2
And as bobpursley noted, the r (distance) is 2 * R.
Try to solve for Fg.
To find the magnitude of the gravitational force of attraction between two uniform spheres of mass M and radius R, we can use the formula:
F = G * ((2 * M^2) / (R^2))
Where:
F is the gravitational force of attraction
G is the gravitational constant (approximately 6.67430 * 10^-11 m^3 kg^-1 s^-2)
M is the mass of each sphere
R is the radius of each sphere
By plugging in the given values, we get:
F = (6.67430 * 10^-11) * ((2 * M^2) / (R^2))
Therefore, the magnitude of their gravitational force of attraction is (6.67430 * 10^-11) * ((2 * M^2) / (R^2)).
To find the magnitude of the gravitational force of attraction between two uniform spheres, we can use Newton's law of universal gravitation, which states that the gravitational force between two objects is given by the equation:
F = G * ((m1 * m2) / r^2)
Where:
F is the gravitational force of attraction,
G is the gravitational constant (approximately 6.67430 × 10^(-11) N.m^2/kg^2),
m1 and m2 are the masses of the two spheres, and
r is the distance between the centers of the spheres.
In this case, both spheres have the same mass (M) and they touch each other, so their centers are a distance of 2R apart.
Substituting these values into the equation, we get:
F = G * ((M * M) / (2R)^2)
Simplifying further:
F = G * (M^2 / 4R^2)
Therefore, the magnitude of the gravitational force of attraction between the two spheres is G * (M^2 / 4R^2), where G is the gravitational constant, M is the mass of each sphere, and R is the radius of each sphere.