2.2. Derive a formula for 'g if it depends upon G, m and r
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Answer:
Explanation:
=> The equation of Force:
f = mg ... (1)
Where,
f = the force acting on the body,
g = the acceleration due to gravity,
m = mass of the body.
=> By the universal law of gravitation:
f = GmM/(r+h)2
In this equation, f is the force between two bodies, G is the universal gravitational constant. It's value is 6.67×10-11 Nm2/kg2. m and M is mass of the object and mass of the earth respectively. r is the radius of the earth.
h is the height at which the body is located from the surface of the earth.
=> As the height (h) is negligibe So,
f = GmM/r2 ...(2)
=> From equation (1) and (2), we get
mg = GmM/r2
⇒ g = GM/r2
Thus, acceleration due to gravity can be written as g = GM/r2
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