Rankers Physics

Planet and Satellite: Practice Problem & Solution

A remote-sensing satellite of earth revolves in a circular orbit at a height of $0.25 \times 10^6\text{ m}$ above the surface of earth. If earth's radius is $6.38 \times 10^6\text{ m}$ and $g = 9.8\text{ m/s}^2$, then the orbital speed of the satellite is: (2015 Re)
$6.67\text{ km/s}$
$7.76\text{ km/s}$
$8.56\text{ km/s}$
$9.13\text{ km/s}$

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Planet and Satellite. Understanding the underlying formula is key to arriving at the correct answer below:

Orbital speed is calculated using $v = \sqrt{\frac{gR^2}{R+h}}$. Substituting the given values for $R$, $h$, and $g$, we get $v \approx 7.76\text{ km/s}$. Therefore, option B is correct.

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