Question

A satellite of \( 10^3 \, \text{kg} \) mass is revolving in a circular orbit of radius \( 2R \). If \[ \frac{10^4 R}{6} \, \text{J} \] energy is supplied to the satellite, it would revolve in a new circular orbit of radius: \[ \text{(use } g = 10 \, \text{m/s}^2, \, R = \text{radius of earth)}. \]

• A. 2.5 R
• B. 3 R
• C. 4 R
• D. 6 R

Answer 1

The Correct Option is D

The total energy is given by \( \text{Total energy} = \frac{-GMm}{2(2R)} \). Upon adding energy \( \frac{10^4R}{6} \), the equation becomes \( \frac{-GMm}{4R} + \frac{10^4R}{6} = \frac{-GMm}{2r} \), where \( r \) denotes the new radius of revolution and \( g = \frac{GM}{R^2} \). Substituting \( g \) and \( m = 10^3\, \text{kg} \), we get \( -\frac{mgR}{4} + \frac{10^4R}{6} = -\frac{mgR^2}{2r} \). This simplifies to \( -\frac{10^3 \times 10 \times R}{4} + \frac{10^4R}{6} = -\frac{10^3 \times 10 \times R^2}{2r} \). Further simplification leads to \( -\frac{1}{4} + \frac{1}{6} = -\frac{R}{2r} \). Solving for \( r \) yields \( r = 6R \).