Two objects are putting gravitational force on each other. One of the objects has its mass reduced to 1/2 of it's original amount while the other object's mass stays the same. By how much is the gravitational force between the two changed? Explain
a
The gravitational force is halved
b
The gravitational force is doubled
c
The gravitational force is quadrupled
d
The gravitational force is cut into one fourth
a) The gravitational force is halved.
The gravitational force between two objects is determined by the masses of the objects and the distance between them. According to Newton's law of universal gravitation, the equation for gravitational force is 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 objects, and r is the distance between them.
In this scenario, one of the object's masses is reduced to 1/2 of its original amount, while the other object's mass stays the same. Let's call the original masses m1 and m2, and the new masses m1' and m2'.
The force between the two objects can be represented as F = G * (m1 * m2) / r^2.
If one of the object's mass is reduced to 1/2 of its original amount, then the new mass can be represented as m1' = (1/2) * m1.
So the new force can be represented as F' = G * (m1' * m2) / r^2.
Substituting the values of m1' and m2 in terms of m1 and m2:
F' = G * ((1/2) * m1) * m2 / r^2
= (1/2) * (G * (m1 * m2) / r^2)
= (1/2) * F
Therefore, the new gravitational force is halved compared to the original gravitational force. Therefore, the answer is a) The gravitational force is halved.