Two objects, with masses m1 and m2, are originally a distance r apart. The gravitational force between them has a magnitude F. The second object has its mass changed to 4m2, and the distance is changed to r/7. What is the ratio between the magnitude of the new gravitational force and F?(G=6.67x10-11N.m2/kg2). You must type your answer as a numerical value.
To find the ratio between the magnitude of the new gravitational force and the initial force, we need to compare the two forces.
1. Start with the formula for gravitational force between two objects:
F = (G * m1 * m2) / r^2
2. Substitute the given values into the formula:
F1 = (G * m1 * m2) / r^2
3. Change the mass and distance for the second object:
m2' = 4m2
r' = r/7
4. Substitute the new values into the formula:
F2 = (G * m1 * (4m2)) / (r/7)^2
To find the ratio, divide F2 by F1:
Ratio = F2 / F1
Now, let's simplify the equation:
F2 = (G * m1 * (4m2)) / (r/7)^2
= (G * m1 * 4m2) / (r^2/49)
= (49 * G * m1 * 4m2) / r^2
By substituting this expression back into the ratio equation, we have:
Ratio = F2 / F1
= ((49 * G * m1 * 4m2) / r^2) / (G * m1 * m2 / r^2)
= (49 * G * m1 * 4m2 * r^2) / (G * m1 * m2 * r^2)
= 49 * 4
= 196
Therefore, the ratio between the magnitude of the new gravitational force and the initial force is 196.