First slide

Variation of g

Question

The weight of an object in the coal mine, sea level and at the top of the mountain are respectively W₁, W₂ and W₃, then

Moderate

A

W₁ < W₂> W₃
B

W₁ = W₂= W₃
C

W₁ < W₂ < W₃
D

W₁ > W₂> W₃

Solution

g at certain depth is g¹ = g(1 -d/R)
Weight in mine is w₁= mg¹ = mg(1-d/R)
weight at sea level w₂ = mg ( acceleration due to gravity is the gravity at sea level)
g at certain height is g¹¹ = GM/(R+h)²
g¹¹ = gR²/(R+h)²
g¹¹= g(1-2h/R)
weight at mountain is w₃ = mg¹¹ = mg(1-2h/R)
w₁< w₂ > w₃

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