A satellite of mass m is circulating around the earth with constant angular velocity. If radius of the orbit is R₀ and mass of the earth M, the angular momentum about the centre of the earth is

The correct option is m√(GMR₀).

To find the angular momentum of the satellite about the centre of the Earth, we can follow these steps:

Step 1: Understand the orbital velocity of the satellite
When a satellite of mass $m$ moves in a circular orbit of radius $R_0$ around the Earth of mass $M$, the gravitational force of attraction between the Earth and the satellite provides the required centripetal force to keep it in orbit.

Therefore, we can write the force balance equation as:
$\frac{GMm}{R_0^2}=\frac{m{v}^2}{R_0}$
where $G$ is the universal gravitational constant and $v$ is the orbital speed of the satellite.

Simplifying the equation to solve for $v$:
$v^2=\frac{GM}{R_0}$
Taking the square root on both sides gives the orbital velocity:
$v=\sqrt{\frac{GM}{R_0}}$

Step 2: Calculate the angular momentum
The angular momentum ($L$) of a particle in a circular orbit about the center of the orbit is given by the formula:
$L=mv{R}_0$

Now, substituting the value of orbital velocity $v$ into the angular momentum equation:
$L=m\sqrt{\frac{GM}{R_0}}{R}_0$

We can bring the radius $R_0$ inside the square root as $R_0^2$:
$L=m\sqrt{\frac{GM{R}_0^2}{R_0}}$

Simplifying the term inside the square root:
$L=m\sqrt{GM{R}_0}$

Thus, the angular momentum of the satellite about the centre of the Earth is $m\sqrt{GM{R}_0}$.