Embibe Experts Solutions for Chapter: Gravitation, Exercise 1: BITSAT 2017

A spherically symmetric gravitational system of particles has mass density $\rho =\left\{\begin{array}{l}{\rho }_0\text{ for }r\le R\\ 0\text{ for }r>R\end{array}\right.$ where, ${\rho }_0$ is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $v$ as a function of distance $r(0<r<\infty )$ from the centre of the system is represented by

A geostationary satellite orbits around the earth in a circular orbit of radius $36000 \mathrm{km}$. Then, the time period of a sky satellite orbiting a few $100 \mathrm{km}$ above the earth's surface $\left(R=64000 \mathrm{km}\right)$ will approximately be