Question

Two planets with equal masses of 6 x 10^24 kg have a gravitational force of 5 x 10^17N.

One of the planets magically increases its mass to 12 x 10^24 kg, The planets' new Fg will be what?

Answer 1

When one planet out of two equal mass planets increases its mass, the new gravitational force between the planets can be calculated using the equation F = Gm1m2/r^2. Plugging in the new mass value into the equation gives a new gravitational force of 4.797 x 10^38 N.

Step-by-step explanation:

The gravitational force between two objects is given by the equation F = Gm1m2/r^2, where F is the force, G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between their centers.

In this case, we have two planets with equal masses of 6 x 10^24 kg and a gravitational force of 5 x 10^17 N. When one of the planets increases its mass to 12 x 10^24 kg, the new gravitational force can be calculated using the same equation. Since the distance between the planets does not change, the only variable that changes is the mass. Plugging in the new mass value and solving for the new force, we get:

F = (6.674 × 10^-11 N·m² kg^2) * (12 x 10^24 kg) * (6 x 10^24 kg) / r^2

F = (6.674 × 10^-11 N·m² kg^2) * (72 x 10^48 kg^2) / r^2

F = 4.797 x 10^38 N

Answer 2

When one of the two equal-mass planets doubles its mass, the new gravitational force between them will also double. Given that the original force was 5 x
`10^1^7`N, the new force would be 10 x
`10^1^7`N or 1 x
`10^1^8`N.

The subject of this question is Physics, specifically relating to gravitational force between two masses. The original gravitational force (Fg) between the two planets with equal masses of 6 x
`10^2^4`kg is given as 5 x
`10^1^7`N. When one of the planets doubles its mass, the new gravitational force can be calculated using the gravitational force equation:

F = G × (m1 × m2) / r2

Since the distance between the two planets remains the same and only the mass of one planet changes, we can calculate the new gravitational force by doubling the numerator of the gravitational force equation:

New Fg = (2 × old Fg)

Therefore, the planets' new gravitational force (Fg) will be:

New Fg = 2 × 5 x
`10^1^7`N = 10 x
`10^1^7`N

This means the gravitational force will double, as one of the masses has doubled.