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The weight of an object in the coal mine, sea level and at the top of the mountain are respectively $W_{1}$ , $W_{2}$ and $W_{3}$ . Then which of the following options is correct?

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

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

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

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

answer is A.

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Detailed Solution

The ratio of weights of an object in the coal mine, at sea level and at the top of the mountain are

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

.
Weight of an object is a product of its mass and acceleration due to gravity. For every object mass is constant and the value of

g

changes according to its height or depth.
The variation of g at depth

d

g_{d} = g (1 - \frac{d}{R})

g

is the acceleration due to gravity at surface of earth =

9.8 m / s^{2}

R

= radius of earth
The variation of g is at height

h

g_{h} = g (1 - \frac{2 h}{R})

For a coal mine at depth

d

and at sea level, and at a height

h

for a mountain, the ratio of weights is

W_{1} : W_{2} : W_{3}

m g_{d} : mg : m g_{h}

mg (1 - \frac{d}{R}) : mg : mg (1 - \frac{2 h}{R})

Hence the ratio is,

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

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