Gravitation

JEE Main level, numerical answer, medium

71 of 223

Question 71 of 223

If the acceleration due to gravity experienced by a point mass at a height hh above the surface of earth is same as that of the acceleration due to gravity at a depth αh(h≪Re)\alpha h\left(h≪{R}_{e}\right) ) from the earth surface. The value of α\alpha will be _____ .
(use Re=6400km{R}_{e}=6400km)

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Answer: 2

Acceleration due to gravity at a height hh above the earth's surface is given by g(1−2hRe)g\left(1-\dfrac{2h}{{R}_{e}}\right)
And acceleration due to gravity at depth dd below the earth surface is given by g(1−dRe)g\left(1-\dfrac{d}{{R}_{e}}\right).
As gabove=gbelow{g}_{above}={g}_{below}
So, g(1−2hRe)=g(1−dRe)g\left(1-\dfrac{2h}{{R}_{e}}\right)=g\left(1-\dfrac{d}{{R}_{e}}\right)
⇒2hRe=dRe\Rightarrow \dfrac{2h}{{R}_{e}}=\dfrac{d}{{R}_{e}}
⇒αh=d\Rightarrow \alpha h=d
Thus, the value of α=2\alpha =2.

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