MHT CET20228 Aug 2022Morning ShiftPhysicsGravitationActual
The mass and radius of the earth and moon are M, R and m, r respectively. The distance between their centers is d . The minimum velocity with which a particle of mass m₀ should be projected from the midpoint between them so that it could reach infinity is
Options
- A2 G d (M+m)
- B2 G m d (M+m)
- C2 2 G d (M+m)
- D2 G m(M+m) d(R+r)
Correct answer
A. 2 G d (M+m)
Step-by-step solution
The potential energy at the midpoint is (- G m m₀ d / 2 - G M m₀ d / 2 ) And suppose ( m₀ V^2 2 ) kinetic energy is required to just send the particle to infinity. On considering energy conservation, i.e., initial total energy is equal to the final total energy: aligned & (- G m m₀ d / 2 - G M m₀ d / 2 )+ ( m₀ V^2 2 )=0 & V^2= 4 G d (M+m) & V=2 G(M+m) d aligned