2) The force of gravity between two masses is 85 N. What will the force become if one mass is increased ten times and the distance between their centres is quadrupled?
Question
- The force of gravity between two masses is 85 N. What will the force become if one mass is increased ten times and the distance between their centres is quadrupled?
Solution
The force of gravity between two masses is given by Newton's law of universal gravitation:
F = G * (m1 * m2) / r^2
where: F is the force between the masses, G is the gravitational constant, m1 and m2 are the masses, r is the distance between the centres of the two masses.
Given that the force (F) is 85 N, one mass is increased ten times (let's say m1 becomes 10m1), and the distance is quadrupled (r becomes 4r), we can substitute these changes into the equation to find the new force (F'):
F' = G * (10m1 * m2) / (4r)^2 = G * (10m1 * m2) / 16r^2 = 10/16 * G * (m1 * m2) / r^2 = 10/16 * F = 0.625 * F
So, the new force will be 0.625 times the original force. If the original force was 85 N, then the new force will be:
F' = 0.625 * 85 N = 53.125 N
So, the force will become approximately 53.125 N if one mass is increased ten times and the distance between their centres is quadrupled.
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