Q89 / 160 · JIPMER 2014 · Physics

Change in acceleration due to gravity is same upto a height $h$ from each other the earth surface and below depth $x$, then relation between $x$ and $h$ is ( $h$ and $x\lt\lt \lt R_e$ )

  • A
    $x=h$
  • Correct answer
    B
    $x=2 h$
  • C
    $x=\frac{h}{2}$
  • D
    $x=h^2$

Solution

Variation in $g$ at a height $h$ from the earth surface $g^{\prime}=g\left(1-\frac{2 h}{R_e}\right)$ Variation in $g$ at a depth $x$ below the earth surface $g^{\prime \prime}=g\left(1-\frac{x}{R_b}\right)$ But variations are same $\therefore \quad g\left(1-\frac{2 h}{R_\theta}\right)=g\left(1-\frac{x}{R_\theta}\right)$ $\therefore \quad x=2 h$

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

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