Question

The value of acceleration due to gravity on the surface of earth is $x$.. At an altitude of ${}^{\prime }{h}^{\prime }$ from the surface of earth, its value is $y$. If $R$ is the radius of earth, then the value of $h$ is

• A. $\left(\sqrt{\frac{x}{y}}-1\right)R$
• B. $\left(\sqrt{\frac{y}{x}}-1\right)R$
• C. $\sqrt{\frac{y}{x}}R$
• D. $\sqrt{\frac{x}{y}}R$

Answer 1

The correct option is B $\left(\sqrt{\frac{y}{x}}-1\right)R$

Value of acceleration due to gravity at height h is $g\times {(1+\frac{h}{R})}^2$

where $g$ is acceleration due to gravity on surface and h is measured from ground

so, $y=x{(1+\frac{h}{R})}^2$

so, $h=(\sqrt{\frac{y}{x}}-1)R$