Question

The critical speed of'a satellite of mass 500 kg is 20 m/s.
What is the critical speed of a satellite of mass 1000 ks
moving in the same orbit?​

Answer 1

✦Question :-

→ Given above ↑

✦Answer :-

$\to \sf \boxed{ \sf u = 20 \sqrt{2} \: \frac{m}{ {s}^{2} } } \:$

❏ Solution :-

According to the question -

mass of satellite = 500 kg

velocity of this satellite ( v ) = 20 m/s

We know that

$\to \: \sf \: v \: = \sqrt{ \frac{ \: G \: m}{r} } \\ \\ \to \sf \: 20 = \sqrt{ \frac{ \:G \: \times 500 }{r} } \\ \\ \bf squaring \: on \: both \: sides \\ \\ \to \sf 400 = \frac{ \:G \times 500 }{r} \: \\ \\ \to \sf r \: = \: \frac{500 \: \times G \: }{400}$

Now ,

mass of another satellite = 1000 kg

orbit is same so that's why radius is same

hence ,

velocity of this satellite ( u) = ?

$\to \sf \: u = \sqrt{ \frac{ \: G \: \times 1000}{r} } \: \\ \\ \to \sf \: u = \sqrt{ \frac{ \: G \: \times 1000}{ \frac{500 \times G }{400} } } \\ \\ \to \sf \: u \: = \sqrt{ \frac{40 \times 1000}{500} } \\ \\ \to \sf u = \sqrt{800} \\ \\ \to \sf \boxed{ \sf u = 20 \sqrt{2} \: \frac{m}{ {s}^{2} } }$

Hope it helps you .