Question

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

Answer 1

Answer: (D)

Here, $g_{d}=\frac{G M}{R^{3}} d=\beta, d < R$ ... (1)
$g_{d}^{\prime}=\frac{G M}{(R+d)^{2}}, d>R$ .... (2)
Using (1), $G M=\frac{\beta R^{3}}{d}$
$g_{d}^{\prime}=\frac{\beta R^{3}}{d(R+d)^{2}}$