Question

Two satellites are heights 1000 km, 2000 km.
Find the ratio of their critical angular speeds.​

Answer 1

Answer:

angular speed is equal to M B square by R then the ratio of of angular speed is is 2 ratio 1

Answer 2

The ratio of their critical angular speeds is $\dfrac{53}{50}$

Explanation:

Given that,

Height of first satellite = 1000 km

Height of second satellite = 2000 km

Suppose the masses of satellite are same.

We need to calculate the orbital speed for first satellite

Using formula of angular speed

$v_{1}=\sqrt{\dfrac{Gm}{(r+h_{1})^2}}$...(I)

We need to calculate the orbital speed for second satellite

Using formula of angular speed

$v_{2}=\sqrt{\dfrac{Gm}{(r+h_{2})^2}}$...(II)

We need to calculate the ratio of their critical angular speeds

Using formula of angular speed

$v=r\omega$

$\omega=\dfrac{v}{r}$

Angular speed for both satellites,

$\dfrac{\omega_{1}}{\omega_{2}}=\dfrac{v_{1}}{v_{2}}=\sqrt{\dfrac{\dfrac{Gm}{(r+h_{1})}}{\dfrac{Gm}{(r+h_{2})^2}}}$

$\dfrac{\omega_{1}}{\omega_{2}}=\sqrt{\dfrac{(R+h_{2})^2}{(R+h_{1})}}$

Put the value into the formula

$\dfrac{\omega_{1}}{\omega_{2}}=\sqrt{\dfrac{(6400+2000)}{(6400+1000)}}$

$\dfrac{\omega_{1}}{\omega_{2}}=\dfrac{106}{100}$

$\dfrac{\omega_{1}}{\omega_{2}}=\dfrac{53}{50}$

Hence, The ratio of their critical angular speeds is $\dfrac{53}{50}$

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Topic :

https://brainly.in/question/7009874