Question

A particle of mass 'm' is kept at rest at a height
3R from the surface of earth, where 'R' is radius of
earth and M is mass of earth. The minimum
speed with which it should be projected, so that it
does not return back, is
(g is acceleration due to gravity on the surface of
earth)
​

Answer 1

Answer:

Ve=[Gm/2R}^1/2

Explanation:

As we know that

Escape velocity ( in terms of radius of planet) -

Vc=sqrt[2GM/R]

Vc=sqrt[2gR]

Vc=Escape velocity

R =Radius of earth

where is

depends on the reference body

  greater the value of M/R or ( gR) greater will be the escape velocity Ve=11.2Km/s  For earth

Ve=sqrt[2Gm]/[R]

=sqrt[2Gm]/[R+h]

=sqrt[2Gm/4R]   where [ h=3R  ]

Ve=[Gm/2R}^1/2