Q 11-04-016NEETJEE MainEAMCET 2011 (Engineering)Medium
The maximum tension a rope can withstand is $60$ kg-wt. The ratio of the maximum accelerations with which two boys of masses $20$ kg and $30$ kg can climb up the rope at the same time is ($g = 10\ \text{m/s}^2$)
Answer: (C) $2 : 1$
$T_{max} = 60 \times 10 = 600$ N. For a boy of mass $m$ climbing with acceleration $a$: $T - mg = ma$.
$20$ kg: $600 - 200 = 20a_1 \Rightarrow a_1 = 20\ \text{m/s}^2$.
$30$ kg: $600 - 300 = 30a_2 \Rightarrow a_2 = 10\ \text{m/s}^2$.
$a_1 : a_2 = 2 : 1$.
Solution by Sreeraj P, M.Sc Physics