By what percent the energy of satallite has to be increased to shift it from an orbit of radius r to $\large\frac{3}{2}$$r $(a)\;66.7 \% \quad (b)\; 33.3\%\quad (c)\;15 \% \quad (d)\;20.3 \%$ 1 Answer energy of satellite in the first case E_1=\large\frac{GMm}{2r} energy in the second case is E_2=\large\frac{GMm}{2\bigg(\Large\frac{3}{2}r \bigg)} \Delta E =\large\frac{GMm}{r} \bigg(\frac{1}{2}-\frac{1}{3}\bigg)=\frac{GMm}{6} \% increase =\large\frac{\Large \frac{GMm}{6r}}{\Large \frac{GMm}{2r}}$$ \times 100$
$\qquad= 33.3 \%$
Hence b is the correct answer

edited Feb 17, 2014 by meena.p