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Does acceleration due to gravity depend upon the mass of the body? |
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Answer» No, acceleration due to gravity do not depend on the mass of the body. Explanation: The acceleration produced in a freely falling body by the gravitational pull of the earth is called the acceleration due to gravitation. We know that, Force = Mass × Acceleration F = m × a a = \(\frac{F}{m}\) ........1 Where F is the force on the object of mass m dropped from a distance r from the centre of earth of mass M. So, force exerted by the earth on the object is F = G\(\frac{M*m}{r^2}\) ...........2 M = Mass of Earth m = mass of object r = distance of object from centre of earth Now, from equation 1 and 2, a = G\(\frac{M*m}{r^2*m}\) a = G\(\frac{M}{r^2}\) Now, from above, a = g = Acceleration due to gravity We also see that, although force is depending on the mass of the object, F = G\(\frac{M*m}{r^2}\) But acceleration due to gravity is independent of the mass. g = G\(\frac{M}{r^2}\) |
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