When a satellite going round earth in a circular orbit of radius r and speed v, losses some of its energy. Then r and v change as

The correct option is: r will decrease and v will increase

To understand why this happens, we can analyze the expressions for the total energy and orbital velocity of a satellite in a circular orbit around the Earth.

Let $M$ be the mass of the Earth, $m$ be the mass of the satellite, and $r$ be the radius of the circular orbit. The total mechanical energy ($E$) of the satellite is the sum of its kinetic energy and gravitational potential energy, which is given by the formula:

$E=-\frac{GMm}{2r}$

where $G$ is the universal gravitational constant. Note that the total energy is negative, indicating a bound system.

When the satellite loses some of its energy (for example, due to atmospheric drag), its total energy $E$ decreases, meaning it becomes more negative. For the value of $E$ to become more negative, the orbital radius $r$ in the denominator must decrease. Therefore, the radius of the orbit $r$ decreases.

The orbital speed $v$ of a satellite in a circular orbit is determined by balancing the gravitational force and the centripetal force:

$\frac{m{v}^2}{r}=\frac{GMm}{r^2}$

Solving for $v$ gives the orbital speed:

$v=\sqrt{\frac{GM}{r}}$

This relation shows that the orbital speed $v$ is inversely proportional to the square root of the orbital radius $r$. Since the orbital radius $r$ decreases, the orbital speed $v$ must increase.

Thus, when the satellite loses energy, its orbital radius $r$ decreases and its orbital speed $v$ increases.