Question

Two satellites revolve around the earth in circular orbits of radii in the ratio 1:2. The ratio of the kinetic energy is

Answer 1

Since nothing is mentioned about the masses of the satellites, I am assuming they both have equal masses i.e m1=m2.

Answer 2

Answer:

The ratio of the kinetic energy is 2:1.

Explanation:

Given that,

Ratio of radius = 1:2

Let be the mass of both satellites is m.

We need to calculate the velocity of satellite

Using formula of orbital velocity

$v_{0}=\sqrt{\dfrac{GM}{r}}$

For first satellite,

$v_{1}=\sqrt{\dfrac{GM}{r}}$

For first satellite,

$v_{2}=\sqrt{\dfrac{GM}{2r}}$

We need to calculate the ratio of the kinetic energy

Using formula of kinetic energy

$\dfrac{K.E_{1}}{K.E_{2}}=\dfrac{\dfrac{1}{2}m_{1}v_{1}^2}{\dfrac{1}{2}m_{2}v_{2}^2}$

Here, $m_{1}=m_{2} = m$

$\dfrac{K.E_{1}}{K.E_{2}}=\dfrac{\dfrac{1}{2}m(\sqrt{\dfrac{GM}{r}})^2}{\dfrac{1}{2}m(\sqrt{\dfrac{GM}{2r}})^2}$

$\dfrac{K.E_{1}}{K.E_{2}}=\dfrac{2}{1}$

Hence, The ratio of the kinetic energy is 2:1.