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How the acceleration due to gravity (g),  and Universal gravitational constant (G), will change as we go to higher altitudes from earth?
1. g increases, G decreases
2. g remains constant, G decreases
3. g decreases, G remains constant
4. g increase, G remains constant

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Correct Answer - Option 3 : g decreases, G remains constant

Concept:

Law of Universal Gravitation

It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.

It is given mathematically as follows:

\(F = \frac{Gm_1m_2}{R^2}\)

Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.

  • The gravitational constant G establishes a relationship between gravitational force, mass, and distance.
    • The value of G is 6.67 × 10-11 N kg-2 m2.

 

Acceleration Due to Gravity:

  • The force of attraction exerted by the earth on a body is called gravitational pull or gravity.
  • We know that when a force acts on a body, it produces acceleration. Therefore, a body under the effect of gravitational pull must accelerate.
  • The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g.
  • The acceleration due to gravity on the surface is given as

\(g = \frac{{GM}}{{{R^2}}} \) -- (1)

G is universal constant, M is mass, R is radius of earth.

Explanation:

So, G is a universal constant, it will remain constant. 

g varies with distance from earth. At some altitude h

\(g = \frac{{GM}}{{{(R+h)^2}}} \)

So, as h increase, the denominator increase, and hence g decreases

So, the g decreases, G remains constant is the correct option. 

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