object weighs 40 N on earth's surface. it would weight on 10 N when its distance from earth's center is

doubled
halved
tripled or
quadrupled

thankyou

Please see your next post, which I saw first.

Sra

To answer this question, we need to understand the relationship between the weight of an object and its distance from the center of the Earth.

The weight of an object is determined by the force of gravity acting upon it. The force of gravity is dependent on the mass of the object and the distance between the object and the center of the Earth.

Mathematically, the weight of an object (W) can be calculated using the formula:

W = mg

where "m" is the mass of the object and "g" is the acceleration due to gravity.

In this case, we are given that the object weighs 40 N on the surface of the Earth. Since weight is a force, it is measured in Newtons (N). Therefore, we can rewrite the formula as:

40 N = mg

Now, let's analyze each scenario:

1. Doubled: If the distance from the center of the Earth is doubled, the force of gravity acting on the object will decrease. According to the inverse square law, the gravitational force is inversely proportional to the square of the distance. Therefore, if the distance is doubled, the force of gravity will be 1/4th (1/2 x 1/2) of the original force. So, in this case, the object would weigh 1/4th of 40 N, which is 10 N.

2. Halved: If the distance from the center of the Earth is halved, the force of gravity acting on the object will increase. Similarly to the previous scenario, the force of gravity is inversely proportional to the square of the distance. Therefore, if the distance is halved, the force of gravity will be 4 times (2 x 2) the original force. So, in this case, the object would weigh 4 times 40 N, which is 160 N.

3. Tripled: If the distance from the center of the Earth is tripled, the force of gravity acting on the object will decrease. Again, considering the inverse square law, the gravitational force is inversely proportional to the square of the distance. So, if the distance is tripled, the force of gravity will be 1/9th (1/3 x 1/3) the original force. Therefore, the object would weigh 1/9th of 40 N, which is approximately 4.44 N.

4. Quadrupled: If the distance from the center of the Earth is quadrupled, the force of gravity acting on the object will decrease further. As per the inverse square law, the gravitational force is inversely proportional to the square of the distance. Hence, if the distance is quadrupled, the force of gravity will be 1/16th (1/4 x 1/4) the original force. So, the object would weigh 1/16th of 40 N, which is 2.5 N.

In summary:

- When the distance from the Earth's center is doubled, the weight of the object becomes 10 N.
- When the distance from the Earth's center is halved, the weight of the object becomes 160 N.
- When the distance from the Earth's center is tripled, the weight of the object becomes approximately 4.44 N.
- When the distance from the Earth's center is quadrupled, the weight of the object becomes 2.5 N.

Remember, these calculations are based on the assumption that the mass of the object remains constant.