Two objects having masses 1: 4 ratio are at rest. When both of them are subjected to same force separately, they achieved same kinetic energy during times t₁ and t₂ respectively. Then ratio of t₁ to t₂ is

Step-by-step solution

After time t ₁ , k ₁= 1 2 ~m v ₁^2= 1 2 ~m ( at ₁ )^2= 1 2 ma ^2 t ₁^2 After time t₂ , aligned & k ₂= 1 2 (4 ~m ) v ₂^2= 1 2 (4 ~m ) ( at ₂ )^2=2 ma ^2 t ₂^2 & ~K ₁= K ₂ 1 2 ma ^2 t ₁^2=2 ma ^2 t ₂^2 t ₁ t ₂ =2 aligned