Q160 / 160 · AP EAMCET 2020 (21 Sep Shift 2) · Physics

Acceleration due to gravity at a height \(h\) is equal to that at a depth \(d\) below the surface of the earth, if

  • A
    \(d=h\)
  • B
    \(2 d=h\)
  • Correct answer
    C
    \(d=2 h\)
  • D
    \(3 d=h\)

Solution

According to question, Acceleration due to gravity at a height \((h)=\) Acceleration due to gravity below depth \((d)\) \(\begin{array}{llll} \Rightarrow & g\left(1-\frac{2 h}{R_e}\right) =g\left(1-\frac{d}{R_e}\right) \\ \Rightarrow & 1-\frac{2 h}{R_e} =1-\frac{d}{R_e} \Rightarrow \frac{2 h}{R_e}=\frac{d}{R_e} \\ \Rightarrow & 2 h =d \end{array}\)

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

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