MHT CET20243 May 2024Morning ShiftPhysicsGravitationActual
Earth has mass ' M₁ ' radius ' R₁ ' and for moon mass ' M ₂ ' and radius ' R ₂ '. Distance between their centres is ' r '. A body of mass ' M ' is placed on the line joining them at a distance r 3 from the centre of the earth. To project a mass ' M ' to escape to infinity, the minimum speed required is
Options
- A[ 2 G r (M₂+ M₁ 2 ) ]^ 1 / 2
- B[ 4 G r (M₁+ M₂ 2 ) ]^ 1 / 2
- C[ 3 G r (M₁+M₂ ) ]^ 1 / 2
- D[ 6 G r ( M ₁+ M ₂ 2 ) ]^ 1 / 2
Correct answer
D. [ 6 G r ( M ₁+ M ₂ 2 ) ]^ 1 / 2
Step-by-step solution
The binding energy of the body is given by aligned B.E. & = GM ₁ M r 3 + GM ₂ M 2 r 3 = 3 GM ₁ M r + 3 GM ₂ M 2 r & = 3 GM r [ M ₁+ M ₂ 2 ] aligned If v is the velocity given to the body, then aligned & 1 2 M v^2= 3 G M r [M₁+ M₂ 2 ] & v= [ 6 G r (M₁+ M₂ 2 ) ]^ 1 2 aligned