Question

The velocity with which a body should be projected from the surface of the earth such that it reaches a maximum hight equal to 5 times radius R of the earth is (M is mass of the earth)​

Answer 1

Answer :

The velocity with which the body should be projected is √5GM/3R

Step-by-step Explanations :

To find : The velocity with which a body should be projected from the

surface of the earth such that it reaches a maximum hight equal

to 5 times radius R of the earth is = ?

From conservation of Energy,

P.E + K.E on the surface of Earth = K.E + P.E at height 5R

∴ -GMm/R + 1/2 × mv² = 0 - GMm/(R + 5R)

1/2 × mv² = GMm/R ( 1 - 1/6 )

= 5GMm/6R

1/2 × mv² = 5GMm/6R

( m and m on both the sides get cancelled )

So we get,

v² = 5GM/6R × 2

v² = 5GM/3R

v = √5GM/3R

Hence the velocity with which the body should be projected is √5GM/3R