Two satellites A and B go round a planet P in circular orbits having radii 4R and R respectively. If the speed of the satellite A is 3V, the speed of the satellite B will be

The correct option is 6 V.

To find the orbital speed of satellite B, we can use the formula for the orbital speed of a satellite in a circular orbit around a planet.

The orbital speed $v$ of a satellite orbiting a planet of mass $M$ at a radial distance $r$ from the center of the planet is given by:
$v=\sqrt{\frac{GM}{r}}$
where $G$ is the universal gravitational constant.

From this formula, we can see that for satellites orbiting the same planet, the orbital speed is inversely proportional to the square root of the orbital radius:
$v\propto \frac{1}{\sqrt{r}}$

Therefore, we can write the ratio of the speeds of satellite A and satellite B as:
$\frac{v_A}{v_B}$

We are given the following values:
- Radius of orbit of satellite A, $r_A=4R$
- Radius of orbit of satellite B, $r_B=R$
- Speed of satellite A, $v_A=3V$

Substituting these values into the ratio equation:
$\frac{3V}{v_B}$

Simplifying the fraction under the square root:
$\frac{3V}{v_B}$

Taking the square root:
$\frac{3V}{v_B}$

Solving for the speed of satellite B ($v_B$):
$v_B=2\times 3V=6V$

Thus, the speed of satellite B will be 6 V.