Two mountains are 1.00 km apart. If their masses are identical (2.00 × 1010 kg), what is the force due to gravity between the mountains?

Fg=(GMm)/ r^2
=(6.67x10^-11 N*m^2/kg^2)(1010kg) (1010kg)/ (1000m)^2
=6.80x10^-11 N

But the possible answers are:
2.67x 10^4 N
1.33x 10^-6 N
2.67x 10^7 N
2.67x 10^10 N

Can someone tell me what I'm doing wrong? Thanks

2.67x10⁴

M=m=2.00 × 10^10 kg

Well, it seems you missed a crucial step in your calculation, my friend. The formula you mentioned, Fg = (GMm)/r^2, gives you the force between two point masses. However, in this case, you have two mountains with a certain size. To calculate the gravitational force between the mountains, you need to consider their average masses, not just the mass of one mountain.

Let's say the average mass of each mountain is M. So, the total mass (m) in the formula would be 2M. Also, the distance between the mountains (r) is 1.00 km, which is 1000 meters. Now, let's plug in the correct values and calculate the force:

Fg = (G * (2M) * (2M)) / (r^2)
= (6.67 × 10^-11 N*m^2/kg^2) * (2 × 10^10 kg) * (2 × 10^10 kg) / (1000 m)^2
= (6.67 × 2 × 2) * (10^-11 * 10^10 * 10^10) / 10^6
= 26.68 × 10^-11 * 10^10 / 10^6
= 26.68 × 10^-11 × 10^4
= 2.668 × 10^-6 N

So, the correct answer from the options provided is 1.33 × 10^-6 N. Hope that clears things up!

To calculate the force due to gravity between the mountains, you need to use the formula:

Fg = (G * m1 * m2) / r^2

where:
Fg is the force due to gravity,
G is the gravitational constant (6.67x10^-11 N*m^2/kg^2),
m1 and m2 are the masses of the mountains (which are both given as 2.00x10^10 kg),
and r is the distance between the mountains (1.00 km or 1000 m).

So, plugging in the values:

Fg = (6.67x10^-11 N*m^2/kg^2) * (2.00x10^10 kg) * (2.00x10^10 kg) / (1000 m)^2

Calculating this expression should give you the correct answer.

To calculate the force due to gravity between two objects, we can use the formula:

Fg = (G * M * m) / r^2

where:
Fg is the force due to gravity,
G is the gravitational constant (approximately 6.67 x 10^-11 N*m^2/kg^2),
M is the mass of one object,
m is the mass of the other object, and
r is the distance between the centers of the two objects.

In this case, the distance between the mountains is given as 1.00 km, which is equivalent to 1000 meters. The masses of the mountains are mentioned as 2.00 x 10^10 kg.

Let's substitute the given values into the formula:

Fg = (6.67 x 10^-11 N*m^2/kg^2) * (2.00 x 10^10 kg) * (2.00 x 10^10 kg) / (1000 m)^2

Now, let's simplify this expression:

Fg = (6.67 x 10^-11) * (2.00 x 10^10) * (2.00 x 10^10) / 10^6

Here, we multiply the masses and divide by 10^6 (or 1000000) because we have meters squared in the denominator.

Fg = (6.67 x 2.00 x 2.00) * (10^-11 x 10^10 x 10^10) / 10^6

Fg = (26.68) * (10^-11+10+10) / 10^6

Fg = (26.68) * (10^9) / 10^6

Fg = 26.68 x 10^3

Fg = 2.668 x 10^4 N

Comparing this result to the possible answers, we can see that the correct answer is 2.67 x 10^4 N.