Question
Download Solution PDFThe acceleration due to gravity at the surface of the earth (mass M and radius R) is proportional to __________.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFThe correct answer is M/R2.
Key Points
- The force acting on an object due to gravity is given by f = mg.
- Where f is the force acting on the object, g is the acceleration due to gravity, and m is the mass of the object.
- According to the law of universal gravitation,
- f = GmM/(r+h)2.
- Where,
f = force between two bodies,
G = universal gravitation constant (6.67×10-11 Nm2/kg2)
m = mass of an object,
M = mass of earth,
r = radius of the Earth.
h = height the object is from the earth's surface. - Since the height (h) is negligible relative to the radius of the earth, we repeat the equation as follows,
f = GmM/r2 - Now balance the two expressions,
mg = GmM/r2
⇒ g = GM /r2 - Therefore, the formula for the acceleration due to gravity is given by, g = GM/r2
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