Two planets A and B having masses m₁ and m₂ move around the sun in circular orbits of r₁ and r₂ radii respectively. If angular momentum of A is L and that of B is 3 ~L , the ratio of time period ( T_A T_B ) is:

Step-by-step solution

aligned & r ₁^2 ~T _ A = L 2 ~m ₁ .(1) & r ₂^2 ~T _ B = 3 ~L 2 ~m ₂ .(2) & T _ A T _ B =3 m ₁ ~m ₂ ( r ₁ r ₂ )^2 & ( T _ A T _ B )^2= ( r ₁ r ₂ )^3 ( r ₁ r ₂ )^2= ( T _ A T _ B )^ 4 3 & 1 27 ( m ₂ ~m ₁ )^3= ( T _ A T _ B ) aligned