Test: Gravitation (August 8) - NEET MCQ

Gravity does not depend upon shape and size of the celestial body. It depends only on the mass of the two bodies and distance between them.
Fold = GmM/R² and Fnew = GmM/R²

If a planet is orbiting the sun then |U|> |K| else it will leave the system because it won’t be under the influence of the sun’s gravity.

Kinetic Energy of the Satellite =GMm​/2r
Potential Energy of the satellite =−GMm​/r 
Total Energy of the Satellite =−GMm​/2r
Hence, Kinetic Energy Cure will be above 0 , hence X 
Potential energy will be the lowest curve , hence Y 
Total Energy is the curve is below 0 , but higher magnitude than Potential Energy  . Hence, Z

The total energy of the system remains constant.

Due to air drag some mechanical energy of satellite will converted into heat energy, there will be loss of ME of satellite, so radius of orbit will decrease and satellite will follow a spiral path towards earth. 
If r is decreases,
P.E.=−GMm​/r, P.E. is also decreases.
K.E=GMm​/2r K.E increasing, increased speed in spite of decrease in M.E. But rate of P.E decreases is more than the rate at which M.E decreases.
Angular momentum L=mrv=mr√GM​r=m√GMr​⇒L∝√r​.
So, angular momentum decreases as r decreases.

Let’s see the formulae for each quantity given there,
Gravitational potential energy  =−GMm/r​
angular velocity =(GM/r³​)^0.5
linear orbital velocity  =(GM/r​)^0.5
centripetal acceleration  =GM/ r²
We can observe that, the quantities in the options B,C,D are all indirectly proportional to r
i.e. ω, v, a α(1/rⁿ)​ where n is a distinct positive integer in each quantity.
So, with increase in r all these quantities decrease.
Now, (-potential energy) α(1/r)​ i.e. negative of potential energy decreases with increase in r. Therefore, potential increases with increase in orbital radius.