Gravitational force between two point masses m1
and m2
placed at a distance r is given by
1 2
2
Gm m F
r
= ; where G is an universal constant. An
object of mass M is divided into two parts, which
are placed at distance r. Find the mass of both parts
if gravitation force of attraction is maximum
between them.
To find the mass of both parts of the object when the gravitational force of attraction is maximum between them, we need to maximize the gravitational force equation:
F = (G * M1 * M2) / r^2
Here, M1 and M2 represent the masses of the two parts of the object, and r is the distance between them.
To maximize the gravitational force, we need to consider the following:
1. The masses of the two parts of the object should be equal. Let's call the mass of each part as M1 and M2.
2. The distance between the two parts should be minimized. Let's call this distance r.
Considering these conditions, we have:
M1 = M2 (the masses of the two parts are equal)
r = distance between the parts
Now, we substitute these values back into the gravitational force equation:
F = (G * M1 * M2) / r^2
= (G * M * M) / r^2 (substituting M1 = M2 = M)
Since we want to maximize the gravitational force, we need to maximize the numerator (G * M * M) while minimizing the denominator (r^2).
Therefore, to maximize the gravitational force of attraction between the two parts of the object, both parts should have the same mass (M) and should be placed at the minimum possible distance (r).
the product of two numbers is maximum when they are the same.
Just as the area of a rectangle with a given perimeter is maximum when it is a square.
and write the law as
F = Gm1*m2/r^2
if you want to be able to read it.