If acceleration due to gravity at distance d[ < R] from centre of earth is β , then its value at

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7.Gravitation

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If acceleration due to gravity at distance $d[ < R]$ from the centre of earth is $\beta$, then its value at distance $d$ above the surface of earth will be [where $R$ is radius of earth]

A

$\frac{\beta R^2}{(R+d)^3}$

B

$\frac{\beta R}{2 d}$

C

$\frac{\beta d}{(R+d)^2}$

D

$\frac{\beta R^3}{d(R+d)^2}$

Solution

(d)

Here, $g_d=\frac{G M}{R^3} d=\beta, d < R \ldots (1)$

$g_d^{\prime}=\frac{G M}{(R+d)^2}, d > R \ldots (2)$

Using $(1)$, $G M=\frac{\beta R^3}{d}$

$g_d^{\prime}=\frac{\beta R^3}{d(R+d)^2}$

Standard 11

Physics

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