Q 11-04-177JEE MainJEE Main 2021 (27 Aug, Shift 2)Medium
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. $(g = 10\ \text{m s}^{-2})$
Answer: (D) $0.4$ s
The $8$ kg box hangs from a movable pulley supported by two segments of the string, so if it moves down by $x$ the $2$ kg box rises by $2x$: $a_2 = 2a$.
For the $8$ kg box: $80 - 2T = 8a$. For the $2$ kg box: $T - 20 = 2(2a) = 4a$.
Adding twice the second to the first: $80 - 40 = 16a \Rightarrow a = 2.5$ m s$^{-2}$.
$0.2 = \frac{1}{2}(2.5)t^2 \Rightarrow t^2 = 0.16 \Rightarrow t = 0.4$ s.
Solution by Sreeraj P, M.Sc Physics