The velocity with which a projectile must be fired so that it escape earth's gravitational does not depend on

Options

A. mass of the earth
B. radius of the projectile's orbit
C. mass of the projectile
D. gravitational constant

Answer

C

Explanation

At a certaing velocity projection, the body will go out of the gravitational field of the earth and will never return to the earth. Thic initial velocity is called escape velocity. The kinetic energy given to the body should be equal to potential energy for body to escape. i.e., potentiial energy=kinetic energy
`+(GM_(e)m)/R=1/2mv_(e)^(2)`
Where `m` is mass of projectile, `M_(e)` is mass of earth, `G` is gravitational constant, `R` is radius.
`:. v_(e)=sqrt((2GM_(e))/(R_(e)))`
The above formula shows that escape velocity is independent of the mass of the projectile.