The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. g = 10 m s - 2

Step-by-step solution

( ( m ₁ ~g -2 ~T )= m ₁ a -(1) ) ( T - m ₂ ~g = m ₂(2 a ) ) (2 ~T -2 ~m ₂ ~g =4 ~m ₂ a -(2) ) ( m ₁ ~g -2 ~m ₂ ~g = ( m ₁+4 ~m ₂ ) a ) ( a = (8-4) g (8+8) = 4 16 ~g = g 4 ) ( a = 10 4 ~m / s ^2 ) ( ~S = 1 2 at ^2 ) ( 0.2 2 4 10 = t ^2 ) ( t =0.4 sec )