Question

A 90 kg body placed at \( 2R \) distance from the surface of the earth experiences gravitational pull of:
(\( R \) = Radius of Earth, \( g = 10 \, \text{ms}^{-2} \)).

• A. 300 N
• B. 225 N
• C. 120 N
• D. 100 N

Answer 1

The Correct Option is D

1. Calculate Gravitational Acceleration at 2R from the Earth’s Surface:
The gravitational acceleration \( g \) at a height \( h \) from the Earth’s surface is given by:
\[ g = g_s \left(1 + \frac{h}{R}\right)^{-2}, \] where \( g_s \) is the gravitational acceleration at the Earth’s surface and \( R \) is the Earth’s radius.
2. Substitute \( h = 2R \):
\[ g = g_s \left(1 + \frac{2R}{R}\right)^{-2} = g_s (3)^{-2} = \frac{g_s}{9}. \] Here, \( g_s = 10 \, \text{m/s}^2 \).
3. Calculate the Gravitational Force:
The gravitational force \( F \) acting on the 90 kg body is:
\[ F = mg = 90 \times \frac{g_s}{9} = 90 \times \frac{10}{9} = 100 \, \text{N}. \]

Answer: 100 N