Question

16. The orbital velocity for an earth bound satellite is 'V'. Then the orbital velocity
for another planet having thrice the mass and one third the radius of the earth
​

Answer 1

Answer:

Given that orbital velocity of earth is V.

Also,

we know that,

$Orbital \: Velocity = \dfrac{GM}{r}$

So,

orbital velocity of planet having thrice the mass of earth and one third the radius of the earth

i.e.

M '= 3M

r' = 1/3 r

So,

$V'=\sqrt{ \dfrac {GM'}{r' }}$

$V' = \sqrt{ \dfrac{ G \times 3M}{ \tfrac{1}{3} {r} }} \\ \\ = \sqrt{\dfrac{3GM}{ \frac{1}{3} {r} }} \\ \\ = \sqrt{ \frac{9GM }{ {r} } } \\ = \sqrt{ \frac{ GM }{ {r}}} \times 3$

So,

$V' = 3V$

where V' is orbital velocity of planet and V each orbital velocity of Earth .