$A$ body moves in a circular orbit of radius $R$ under the action of a central force. The potential due to the central force is given by $V(r) = kr$ ($k$ is a positive constant). The period of revolution of the body is proportional to:

Describe the method for drawing an ellipse and explain the foci of an ellipse,midpoint,and semi-major axis.

$A$ planet of mass $M$ has two natural satellites with masses $m_1$ and $m_2$. The radii of their circular orbits are $R_1$ and $R_2$ respectively. Ignore the gravitational force between the satellites. Define $v_1, L_1, K_1$ and $T_1$ to be,respectively,the orbital speed,angular momentum,kinetic energy,and time period of revolution of satellite $1$; and $v_2, L_2, K_2$ and $T_2$ to be the corresponding quantities of satellite $2$. Given $m_1/m_2 = 2$ and $R_1/R_2 = 1/4$,match the ratios in List-$I$ to the numbers in List-$II$.

List-$I$	List-$II$
$P. \frac{v_1}{v_2}$	$1. \frac{1}{8}$
$Q. \frac{L_1}{L_2}$	$2. 1$
$R. \frac{K_1}{K_2}$	$3. 2$
$S. \frac{T_1}{T_2}$	$4. 8$

$A$ satellite of mass $m$ is revolving around the Earth of mass $M$ in an orbit of radius $r$ with constant angular velocity $\omega$. The angular momentum of the satellite is ($G$ = gravitational constant).

$A$ satellite of the earth is revolving in a circular orbit with a uniform speed $v$. If the gravitational force suddenly disappears,the satellite will

$A$ satellite of the earth is revolving in a circular orbit with a uniform velocity $V$. If the gravitational force suddenly disappears,the satellite will