Question

Two artificial satellites of masses 'm' and '6m' orbit the earth in circular orbits of radii 'r' and '4r' respectively. The ratio of their orbital speeds is:

• A.
  $\frac{1}{2}$
• B.
  4
• C. $\sqrt{2}$
• D. 2

Answer 1

The correct option is D 2

Given,
Mass of 1st satellite $\left(m_1\right)$ = m
Mass of 2nd satellite $\left(m_2\right)$= 6m
Radius of orbit of 1st satellite $\left(r_1\right)$ = r
Radius of orbit of 2nd satellite $\left(r_2\right)$= 4r

The orbital speed of a satellite: $v^{}=\sqrt{\frac{GM}{r^{}}}$
where, r is the orbital radius of a satellite and M is the mass of the earth.
As we can see, orbital velocity is independent of the mass of the satellite.
So,
Orbital velocity of 1st satellite: $v_1=\sqrt{\frac{GM}{r_1}}$
Orbital velocity of 2nd satellite:
$v_2=\sqrt{\frac{GM}{r_2}}$
Therefore, the ratio of orbital velocities of 1st satellite to 2nd satellite:
$\frac{v_1}{v_2}=\sqrt{\frac{r_2}{r_1}}=\sqrt{\frac{4r}{r}}=\sqrt{4}=2$
Hence, the required ratio is 2