The weight of an object in the coal mine, sea level, at the top of the mountain are $W_{1}, W_{2}$ and $W_{3}$ respectively, then

W_{1} < W_{2} > W_{3}

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W_{1} = W_{2} = W_{3}

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W_{2} > W_{1} > W_{3}

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W_{1} > W_{2} > W_{3}

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Solution

The correct option is A $W_{1} < W_{2} > W_{3}$
A we know that the weight is given by $W = m g$

On changing the $g$ , weight also changes.

(1) Weight in the coal mine-
$W_{1} = m g^{'}$
Acceleration due to gravity below the earth surface, $g^{'} = g (1 - \frac{d}{R})$
$∴ W_{1} = m g [1 - \frac{d}{R}]$

(2) Weight at sea level- Here weight is equal to the weight at earth surface i.e
$W_{2} = m g$

(3) Weight at the top of the mountain
$W_{3} = m g^{'}$
Acceleration due to gravity above the earth surface
$g^{'} = g {(1 - \frac{h}{R})}^{- 2} = g [1 - \frac{2 h}{R}]$
So, $W_{3} = m g [1 - \frac{2 h}{R}]$

Therefore, $W_{1} < W_{2} > W_{3}$

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

The weight of an object in the coal mine, sea level, at the top of the mountain are $W_{1}, W_{2}$ and $W_{3}$ respectively, then