NEETPhysicsGravitation
The escape velocity on the surface of planet A is 4 times the escape velocity on the surface of planet B . If the mass of planet A is 8 times the mass of planet B , then the ratio of their radii ( R_A R_B ) is :
Options
- A2
- B1 4
- C1 2
- D4
Correct answer
C. 1 2
Step-by-step solution
The escape velocity of a planet is given by v = 2GM R . Taking the ratio of the escape velocities for planets A and B : v_A v_B = M_A M_B R_B R_A We are given that v_A v_B = 4 and M_A M_B = 8 . Substituting these values into the equation gives: 4 = 8 R_B R_A Squaring both sides: 16 = 8 R_B R_A R_B R_A = 16 8 = 2 Therefore, the ratio of their radii is: R_A R_B = 1 2 Answer: 1 2