PYQ NEET- (Galilean & Kepler) Laws & Centripetal Forces

• 2017: The kinetic energy of the satellite is given by:

$$ K = \frac{1}{2}mv^2 $$

where m is the mass of the satellite and v is its velocity. The gravitational force between the satellite and the earth is given by:

$$ F = \frac{GMm}{r^2} $$

where G is the gravitational constant, M is the mass of the earth, and r is the distance between the satellite and the earth.

The kinetic energy of the satellite is related to the gravitational potential energy by:

$$ F = \frac{GmM}{r^2} $$

where a is the acceleration of the satellite.

Substituting this into the equation for kinetic energy, we get:

$$ K = \frac{1}{2}mv^2 = \frac{1}{2}m\left(\frac{GM}{r}\right) = \frac{GMm}{2r} $$

Therefore, the kinetic energy of the satellite is:

$$ K = \frac{GMm}{r}