MHT CET202411 May 2024Evening ShiftPhysicsGravitationActual
A body is projected in vertically upward direction from the surface of the earth of radius ' R ' into space with velocity ' n V_ c ' (n 1) . The maximum height from the surface of earth to which a body can reach is
Options
- An^2 R (1-n^2 )
- Bn ^2 R ^2 (1- n )
- CnR ^2 (1+ n ^2 )
- Dn^2 R^2 (1+n)
Correct answer
A. n^2 R (1-n^2 )
Step-by-step solution
aligned & array l As per the law of conservation of energy, (K . E+P . E)_ surface =(K . E+P . E)_ max height array & -G M m R + 1 2 m (n V_e )^2=- G M m R+h + 1 2 m(0)^2 & 1 2 m (n V_e )^2=G M m ( 1 R - 1 R+h ) & (n V_e )^2=2 G M ( R+h-R R(R+h) ) & (n V_e )^2=V_e^2 ( h (R+h) ) aligned array ll & 1 n^2 = R h +1 & R h = 1-n^2 n^2 & h= n^2 R (1-n^2 ) array