A lead sphere of mass' m ' falls in a viscous liquid with terminal velocity ' V ' Another lead sphere of mass ' 8 ~m ' will fall through the same liquid with terminal velocity

Step-by-step solution

The terminal velocity is given by, aligned & V _ T = 2 9 r ^2 ( - ) & V _ T r ^2 aligned where r radius sphere aligned & Mass volume m ₁ ~m ₂ = ( 4 3 r ₁^3 ) ( 4 3 r ₂^3 ) m 8 ~m = r ₁^3 r ₂^3 & 1 8 = ( r ₁ r ₂ )^3 r ₁ r ₂ = 1 2 r ₂=2 r ₁ & So V _ T 2 ~V _ T 1 = r ₂^2 r ₁^2 =4 V _ T 2 =4 ~V _ T 1 =4 ~V _ T aligned