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. (use g = m/s²)

Let tension in the string attached to 2 kg mass be T,
Tension in the string attached to 8 kg mass is 2T

Using constraint equations,
If the acceleration of 8 kg mass is a, then the acceleration of 2 kg mass is 2a

Free body diagram of masses can be drawn as,

From Newton's second law,

8g−2T=8a…(i)

T−2g=4a…(ii)

on substitution, we get,

8g−2(2g+4a)=8a

4g=16a

a=2.5 ms−2

Now, from S=ut+1/2at2

0.2=1/2(2.5)t2

4/25=t2

t=2/5=0.4 s