Question

If the radius of a planet is r and its density is p the escape velocity from its surface will be

Answer 1

Answer:

The formula to find escape velocity is v = sqrt(2GM/r). M is the mass of the earth, G is the gravitational constant, r is the earths radius, and v is escape velocity.

Answer 2

The Escape velocity will be Ve = $R\sqrt{\frac{8G\pi p}{3} }$

Explanation:

To find the value of escape velocity , Let us consider the planet as a spherical form then the Volume will be V = 4/3πR³p

Then we know the density p = M/V

Where M is the mass and V is the volumne

Mass M = pV = 4/3πR³p

Then the Escape velocity will be

Ve = $\sqrt{\frac{2GM}{R}$

Ve = $\sqrt{\frac{2G}{R} }(\frac{4\pi }{3} R^{3}p)$

Ve = $R\sqrt{\frac{8G\pi p}{3} }$

Ve∝ $\sqrt{pR}$ is the escape velocity

Where p is the density and R is the radius of the sphere