Q 11-04-202JEE MainJEE Main 2018 (8 Apr)Medium
Two masses $m_1 = 5$ kg and $m_2 = 10$ kg, connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is $0.15$. The minimum weight $m$ that should be put on top of $m_2$ to stop the motion is:
Answer: (C) $27.3$ kg
To stop the moving system, the kinetic friction on $m_2 + m$ must exceed the pull of the hanging mass:
$$\mu(m_2 + m)g > m_1g \;\Rightarrow\; 0.15(10 + m) > 5 \;\Rightarrow\; m > 23.3\ \text{kg}$$
Any added mass above $23.3$ kg decelerates the system to rest (after which static friction holds it). Of the given options, $10.3$ kg and $18.3$ kg are too small; the smallest that works is $27.3$ kg.
Solution by Sreeraj P, M.Sc Physics