If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth $\alpha \mathrm{h}$ ( $\mathrm{h} \ll \mathrm{R}_{\mathrm{e}}$ ) from the earth surface. The value of $\alpha$ will be \_\_\_\_ . (use $\mathrm{R}_{\mathrm{e}}=6400 \mathrm{~km}$ )

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Gravitation

If the acceleration due to gravity experienced by a point mass at a height h above the surface of earth is same as that of the acceleration due to gravity at a depth

α h

(

h ≪ R_{e}

) from the earth surface. The value of

α

will be ____ .
(use

R_{e} = 6400 km

)

Answer: 2

Solution

At height

h

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

(for

h ≪ R

). At depth

d

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

. Equating:

1 - \frac{2 h}{R} = 1 - \frac{d}{R}

, so

d = 2 h

. Since

d = α h

, we have

α = 2

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Integer answer

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