NEET2013PhysicsGravitationActual
The radius of planet is twice the radius of earth. Both have almost equal averge mass densities V_P and V_E are escape velocities of the planet and the earth respectively, then:
Options
- AV_P=1.5 V_E
- BV_P=2 ~V _ E
- CV_E=3 ~V _ P
- DV_E=1.5 ~V _ P
Correct answer
B. V_P=2 ~V _ E
Step-by-step solution
According to the question R_P=2 R_E, _E= _P Escape velocity of earth aligned V_E & = 2 G M_E R_E = 2 G R_E ( 4 3 R_E^3 _E ) & =R_E 8 3 G _E aligned Similarly Escape velocity of planet aligned V_P & = 2 G M_P R_P = 2 G R_P ( 4 3 R_p ^3 _p ) & =R_P 8 3 G _p aligned from eq. (i) and eq. (ii) V_E V_P = R_E R_P _E _P = R_E 2 R_E _Q _E = 1 2 (given) V_p=2 V_E