The weights of an object are measured in a coal mine of depth ' h₁ ', then at sea level of height ' h₂ ' and lastly at the top of a mountain of height ' h₃ ' as W₁, W₂ and W₃ respectively. Which one of the following relations is correct? [ h₁ R, h₃ h₂ = R, R = radius of the earth ] (a) W₁ = W₂ = W₃ (b) W₁ W₂ W₃

Answer: (d). g is maximum at the surface (sea level). Inside the mine: gd = g(1 - h₁/R) W₃.

The weights of an object are measured in a coal mine of depth ' h₁ '… | MHT CET 2024 (15 May, Shift 1)

Q41MHT CET 2024 · 15 MAY · SHIFT 1Medium

Acceleration Due to Gravity

The weights of an object are measured in a coal mine of depth ' $h_1$ ', then at sea level of height ' $h_2$ ' and lastly at the top of a mountain of height ' $h_3$ ' as $W_1, W_2$ and $W_3$ respectively. Which one of the following relations is correct? [ $h_1 \ll R, h_3 \gg h_2 = R, R =$ radius of the earth ]

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Answer: (d)

$g$ is maximum at the surface (sea level).
Inside the mine: $g_d = g\left(1 - \frac{h_1}{R}\right) < g$ , so $W_1 < W_2$
On the mountain: $g_h = g\left(\frac{R}{R+h_3}\right)^2 < g$ , so $W_3 < W_2$
So the answer is (d) $W_1 < W_2 > W_3$ .

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