Question

Check the correctness of the following relation V = 2 GM/R, where V is escape velocity, G is the gravitational constant, M is mass, and R is the radius.

a) The relation is correct.
b) The relation is incorrect.

Answer 1

The student's relation V = 2 GM/R is incorrect; the correct relation for escape velocity is Vesc = √(2GM/R), where G represents the gravitational constant, M is the mass of the celestial body, and R is the radius.

Step-by-step explanation:

The relation V = 2 GM/R is incorrect. The correct formula for escape velocity (Vesc) is derived from setting the total mechanical energy of the system to zero, taking into account both kinetic and potential energy at the initial point and the point at infinity where kinetic energy is zero and gravitational potential energy is negligible.

The correct formula for escape velocity is Vesc = √(2GM/R), where:

• G is the gravitational constant
• M is the mass of the celestial body
• R is the radius at which the escape velocity is being calculated

In conclusion, answer (b) the relation is incorrect, since the escape velocity is proportional to the square root of (2GM/R), not 2GM/R directly.