we know that f=m1m2/d(to the power 2)

if f1=m1m2/d(to the power2) and f2=m1m2/D(to the power 2);

then, f1>f2 if d

we also know that f=m*a;

therfore similarly; a1>f2;

from this we can conclude that with the decrease in the distance the acceleration is increasing if mass is constant.

now , if we consider a body with mass atleast half of the mass of the earth ,then as its distance decreases the acceleration should increase..but then how is accelaeration due to gravity constant........

To address your question, we need to delve into the concepts of gravitational force and acceleration due to gravity. You’ve correctly stated the gravitational force equation, which is given by Newton's law of universal gravitation: F = (m1 * m2) / d². Here, F is the gravitational force between two masses, m1 and m2, and d is the distance between their centers. You also mentioned the relationship between force and acceleration, F = m * a, which is Newton's second law of motion. Let's break this down further.

Understanding Gravitational Force and Acceleration

When you say that f1 > f2 if d < D, you are highlighting that as the distance between two masses decreases, the gravitational force increases. This is indeed true. However, when we talk about the acceleration due to gravity, we need to consider the context of a specific mass, particularly when we are near a massive body like Earth.

Acceleration Due to Gravity

The acceleration due to gravity at the surface of the Earth is approximately 9.81 m/s². This value is derived from the gravitational force acting on an object of mass m near the Earth's surface, where the mass of the Earth is M and the radius of the Earth is R. The formula for gravitational acceleration g can be expressed as:

• g = G * M / R²

Here, G is the gravitational constant. This equation shows that the acceleration due to gravity is constant at the surface of the Earth because both M (the mass of the Earth) and R (the radius of the Earth) are constant values.

What Happens When Distance Changes?

Now, if we consider a body with mass at least half that of the Earth, as you mentioned, and we decrease the distance between this body and another mass, the gravitational force between them will indeed increase. However, the acceleration due to gravity experienced by an object near this massive body will depend on the mass of that body and the distance from its center.

Why is Acceleration Due to Gravity Constant Near Earth?

When we say that the acceleration due to gravity is constant near the Earth's surface, we are referring to a specific range of distances (essentially, within a few kilometers of the surface). At these distances, the change in d (the distance from the center of the Earth) is negligible compared to the radius of the Earth. Therefore, g remains approximately constant.

However, if you were to move significantly away from the Earth's surface or towards a massive body, the distance would start to affect the gravitational force and, consequently, the acceleration due to gravity. For example, if you were to travel far away from the Earth, d would increase, causing g to decrease according to the inverse square law.

In Summary

In essence, while it is true that gravitational force increases as distance decreases, the acceleration due to gravity remains constant at the Earth's surface due to the relatively small changes in distance compared to the Earth's radius. If you were to consider larger distances or different masses, then yes, the acceleration would vary. This is why we observe a constant acceleration due to gravity near the Earth's surface, while also recognizing that it can change with distance and mass in other scenarios.

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