Q123 / 180 · COMEDK 2014 · Physics

The value of $g$ at a height equal to half the radius of the earth from the earth's surface is

  • A
    $\frac{g}{2}$
  • B
    $\frac{g}{3}$
  • Correct answer
    C
    $\frac{4 g}{9}$
  • D
    $\frac{g}{4}$

Solution

The value of $g$ at height $h$ from the surface of the earth is given as $$ \begin{aligned} g_{h} &=\frac{g}{\left(1+\frac{h}{R_{e}}\right)^{2}} \\ &=\frac{g}{\left(1+\frac{R_{e} / 2}{R_{e}}\right)^{2}} \quad\left(h=\frac{R_{e}}{2}\right) \\ &=\frac{g}{\left(1+\frac{1}{2}\right)^{2}}=\frac{4 g}{9} \end{aligned} $$

Hence, the correct answer is option: 'C'.

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