MHT CET202019 Oct 2020Evening ShiftPhysicsGravitationActual
Earth has mass ' M ₁ ^ and Radius ' R ₁ ^ . Moon has 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 ata distance r 3 from centre of the earth. To project the mass ' M ^ to escape to infinity, the minimum speed required is
Options
- A[ 6 G r ( M ₁- M ₂ 2 ) ]^ 1 2
- B[ 6 G r ( M ₁+ M ₂ 2 ) ]^ 1 2
- C[ 3 G r ( M ₁+ M ₂ 2 ) ]^ 1 2
- D[ 3 G r ( M ₁- M ₂ 2 ) ]^ 1 2
Correct answer
B. [ 6 G r ( M ₁+ M ₂ 2 ) ]^ 1 2
Step-by-step solution
(C) The binding energy of the body is given by B.E. aligned &= G M₁ M r 3 + G M₂ M 2 r 3 &= 3 G M₁ M r + 3 G M₂ M 2 r &= 3 G M r [M₁+ M₂ 2 ] aligned If V is the velocity given to the body, then aligned & 1 2 m V²= 3 G M r [M₁+ M₂ 2 ] & V= [ 6 G r (M₁+ M₂ 2 ) ]^ 1 2 aligned