Two lead spheres of same radius are in contact with each other. The gravitational force of attraction between them is F. If two lead spheres of double the previous radius are in contact with each other, the gravitational force of attraction between them will be:
Question
Two lead spheres of same radius are in contact with each other. The gravitational force of attraction between them is F. If two lead spheres of double the previous radius are in contact with each other, the gravitational force of attraction between them will be:
Solution
The gravitational force between two objects is given by the formula:
F = G * (m1*m2) / r^2
where:
- F is the gravitational force,
- G is the gravitational constant,
- m1 and m2 are the masses of the two objects, and
- r is the distance between the centers of the two objects.
In this case, the two lead spheres are in contact, so r is equal to the diameter of one sphere.
If the radius of the spheres is doubled, the volume (and therefore the mass, since the density is constant) of each sphere is increased by a factor of 2^3 = 8. So m1 and m2 are both 8 times larger.
The distance between the centers of the spheres (r) is also doubled, so r is 2 times larger.
Substituting these changes into the formula gives:
F_new = G * (8m18m2) / (2r)^2 = G * (64m1m2) / (4r^2) = 16 * G * (m1*m2) / r^2 = 16F
So the gravitational force of attraction between the two larger spheres is 16 times the gravitational force of attraction between the two smaller spheres.
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