JEE Mains · Physics · STD 11 - 7. gravitation
The acceleration due to gravity at height \(h\) above the earth if \(h \ll R\) (radius of earth) is given by
- A \(g^{\prime}=g\left(1-\frac{2 h}{R}\right)\)
- B \(g^{\prime}=g\left(1-\frac{2 h^2}{R^2}\right)\)
- C \(g^{\prime}=g\left(1-\frac{h}{2 R}\right)\)
- D \(g^{\prime}=g\left(1-\frac{h^2}{2 R^2}\right)\)
Answer & Solution
Correct Answer
(A) \(g^{\prime}=g\left(1-\frac{2 h}{R}\right)\)
Step-by-step Solution
Detailed explanation
For point outside the surface of earth \(g =\frac{ GM }{ r ^2}\) I = distance from center of earth \(\Rightarrow g ( h )=\frac{ GM }{( R + h )^2} \Rightarrow g ( h )=\frac{ GM }{ R ^2\left(1+\frac{ h }{ R }\right)^2}\)…
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