Question

Which of the following statements are true about escape velocity? I. It is dependent on the mass of the escaping object II. It is dependent on the radius of the object being escaped from III. It is dependent on the radius of the escaping object.

Answer 1

By energy conservation,

KEi + PEi = KEf + PEf

here, KEi = Initial kinetic energy = (1/2)*m*Vesc^2

Vesc = velocity required for object to escape the planet

KEf = final kinetic energy = 0, since final velocity of object will be zero after escaping

PEf = Initial potential energy of object = -G*m*M/R, since they are on the surface of planet

PEi = final potential energy of object = 0 at infinity

Where m = mass of object, M = mass of planet

So, (1/2)*m*Vesc^2 = G*m*M/R

escape velocity = Vesc = sqrt(2*G*M/R)

escape velocity of an object is given by:

V_esc = sqrt (2*G*M/R)

Here G = gravitational constant = 6.67*10^-11

M = mass of planet from which object needs to escape

R = radius of planet from which object needs to be escaped

So we can see that escape velocity does not depends on the mass and radius of escaping object

While it depends on the Mass and radius of planet from which it is trying to escape.

So I and III are wrong

Statement II is correct