The acceleration due to gravity at a height h is given by `g_(h)=g((R )/(R+h))^(2)`, where g is the accleeration due to gravity on the surface of earth. For `h lt lt R`, find the value of g using the Binomial theorem.

Explanation

To find the value of \( g_h \) at a height \( h \) using the Binomial theorem, we start with the formula given:

\[ g_h = g \left( \frac{R}{R+h} \right)^2 \]

where \( g \) is the acceleration due to gravity at the surface of the Earth, \( R \) is the radius of the Earth, and \( h \) is the height above the Earth's surface. We are given that \( h \) is much smaller than \( R \) (i.e., \( h \ll R \)).

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