JEE Main20244 Apr 2024Evening ShiftPhysicsGravitationActual
Correct formula for height of a satellite from earths surface is:
Options
- A( T^2 R^2 4 ^2 g )^ 1 / 3 -R
- B( T^2 R^2 g 4 ^2 )^ 1 / 3 -R
- C( T^2 R^2 g 4 ^2 )^ -1 / 3 +R
- D( T^2 R^2 g 4 )^ 1 / 2 -R
Correct answer
B. ( T^2 R^2 g 4 ^2 )^ 1 / 3 -R
Step-by-step solution
GMm ( R + h )^2 = mv ^2 ( R + h ) GM ( R + h ) = v ^2 ....(1) v =( R + h ) v =( R + h ) 2 T ....(2) GM R ^2 = g GM = gR ^2 ....(3) Put value from (2) & (3) in eq. (1) aligned & gR ^2 ( R + h ) =( R + h )^2 ( 2 T )^2 & T ^2 R ^2 ~g (2 )^2 =( R + h )^3 & [ T ^2 R ^2 ~g (2 )^2 ]^ 1 / 3 - R = h aligned