Question

find the percentage decrease in acceleration due to gravity when a body is taken from the surface of earth to a height of 64km from it's surface

Answer 1

concept of gravitation

Answer 2

percentage decrease in acceleration due to gravity is 2%

acceleration due to gravity of earth depends on height from its surface.

g = g0/(1 + h/r)²

given, h = 64 km, radius of the earth, r = 6400 km

so, g = g0/(1 + 64/6400)² = g0/(1 + 0.01)²

⇒g =g0/(1.01)²

decrease in g, ∆g = g0 - g

= g0 - g0/(1.01)²

= g0[ (1.01² - 1)/(1.01)² ]

now percentage change in acceleration due to gravity, ∆g/g0 × 100 = (1.01² - 1)/(1.01)² × 100 = 1.97 % ≈ 2%

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