Question

If the radius of the Earth is doubled, then what does the value of critical velocity become?

Answer 1

The critical velocity is the minimum velocity required for an object to escape the gravitational pull of a celestial body. It is given by the formula:

$v_c=\sqrt{\frac{2GM}{r}}$

Where:

• $v_c$ is the critical velocity
• $G$ is the gravitational constant
• $M$ is the mass of the celestial body
• $r$ is the distance from the center of the celestial body to the object

If the radius of the Earth is doubled, the new radius would be $2r$. Substituting this value into the formula, we have:

$v_c^{\prime }=\sqrt{\frac{2GM}{2r}}$

Simplifying the expression, we get:

$v$