The weights of an object are measured in a co | vedclass

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(D) The weight of an object is given by $W = mg$,where $m$ is the mass and $g$ is the acceleration due to gravity.At the surface of the earth $(h=0)$,

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$W_1  W_3$

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(D) The weight of an object is given by $W = mg$,where $m$ is the mass and $g$ is the acceleration due to gravity.At the surface of the earth $(h=0)$,the acceleration due to gravity $g$ is maximum.As we move into a mine of depth $h_1$,the acceleration due to gravity is $g_1 = g(1 - h_1/R)$,so $W_1 = mg(1 - h_1/R) As we move to the top of a mountain of height $h_3$,the acceleration due to gravity is $g_3 = g(1 - 2h_3/R)$,so $W_3 = mg(1 - 2h_3/R) Since $W_2$ is the weight at the surface,it is greater than both $W_1$ and $W_3$.Therefore,the correct relation is $W_1  W_3$.

The weights of an object are measured in a coal mine of depth $h_1$,then at sea level of height $h_2=0$,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? [$h_1 \ll R, h_3 \ll R, R=$ radius of the earth]

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