Question

What is the value of acceleration due to gravity at a height equal to half the radius of the Earth, from its surface ?

• A. $4.4\ ms^{-2}$
• B. $6.5\ ms^{-2}$
• C. Zero
• D. $9.8\ ms^{-2}$

Answer 1

The Correct Option is A

The acceleration due to gravity \( g_h \) at a height \( h \) above the Earth's surface is given by the formula: \[ g_h = \frac{g}{\left( 1 + \frac{h}{R} \right)^2} \] where: - \( g \) is the acceleration due to gravity at the Earth's surface (\( g = 9.8 \, \text{m/s}^2 \)) - \( R \) is the radius of the Earth - \( h \) is the height above the surface of the Earth In this case, \( h = \frac{1}{2}R \). Substituting this into the formula: \[ g_h = \frac{g}{\left( 1 + \frac{1}{2} \right)^2} = \frac{g}{\left( \frac{3}{2} \right)^2} = \frac{g}{\frac{9}{4}} = \frac{4g}{9} \] Now, substituting the value of \( g \) (9.8 m/s²): \[ g_h = \frac{4 \times 9.8}{9} = \frac{39.2}{9} = 4.4 \, \text{m/s}^2 \] Thus, the acceleration due to gravity at a height equal to half the radius of the Earth is \( 4.4 \, \text{m/s}^2 \).

Therefore, the correct answer is (A) 4.4 m/s².