Question

Taking the radius of the earth to be $6400km$, by what percentage will the acceleration due to gravity at a height of $100km$ from the surface of the earth differ from that on the surface of the earth?

• A. About 1.5%
• B. About 5%
• C. About 8%
• D. About 3%

Answer 1

Answer: (D)

Here, $R_e=600kmh=100km$
Acceleration due to gravity at height, $h$
$g^{\prime }=\frac{g{R}_e^2}{{\left(R_e+h\right)}^2}$
$g^{\prime }=\frac{g(6400{)}^2}{(6400+100{)}^2}$
$=g{\left(\frac{6400}{6500}\right)}^2$
Percentage change in acceleration due to gravity
$=\frac{g-g^{\prime }}{g}\times 100$
$=\left(1-\frac{g^{\prime }}{g}\right)\times 100\%$
$={\left[1-\frac{6400}{6500}\right]}^2\times 100\%$
$=3.05\%$