Question

an object of mass 2m, at an altitude equal to the moon’s radius, r, above the surface of the moon, is attracted to the moon with a gravitational force of

Answer 1

The gravitational force on an object of mass 2m at an altitude of the moon's radius above its surface is one-fourth of the gravitational force it would experience on the moon's surface, according to Newton's universal law of gravitation.

Step-by-step explanation:

To find the gravitational force of attraction to the moon on an object of mass 2m at an altitude equal to the moon's radius, r, above the surface of the moon, we can use Newton's universal law of gravitation, which states that the force between two masses is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres:

F = G(Mm)/r^2

Here, G is the gravitational constant, M is the mass of the moon, m is the mass of the object, and r is the distance from the object to the centre of the moon. Since the object is at an altitude of r, the total distance between the object and the moon's centre is 2r. Plugging in the values:

F = G(2Mm)/(2r)^2

F = G(Mm)/2r^2

This equation shows that the force of attraction on the object is one-fourth of the force it would experience on the surface of the moon.

Answer 2

To find the gravitational force on an object of mass 2m at an altitude equal to the Moon's radius above its surface, Newton's universal law of gravitation should be applied, taking into account that the distance from the object to the Moon's center is now 2r, leading to the adjusted formula F = GmM/(2r)^2.

Step-by-step explanation:

The question relates to the gravitational force exerted on an object of mass 2m at an altitude equal to the Moon's radius r above its surface. To calculate the gravitational force on the object, we use Newton's universal law of gravitation, which states that the gravitational force F between two masses m and M is given by the equation F = GmM/r2, where G is the gravitational constant, m is the mass of the object, M is the mass of the Moon, and r is the distance from the center of the Moon to the object. Since the object's altitude is equal to the Moon's radius, the distance r will be doubled, changing the original formula to F = G(2m)M/(2r)2 = GmM/(2r)2. Applying the values provided for the Moon's mass and radius along with the gravitational constant, one can solve for the gravitational force F.