Two blocks ($P$ and $Q$) with respectively masses $2$ kg and $1.5$ kg are joined by a massless thread. These blocks are mounted on a frictionless pully which is fixed on the edge of a cube ($S$), as shown in the figure below. Block $P$ is positioned on the top surface which has no friction and block $Q$ is in contact with side-surface, having coefficient friction $\mu$. The cube ($S$) moves towards the right with acceleration of $\dfrac{g}{2}$, where $g$ is gravitational acceleration. During this movement the block $P$ and $Q$ remain stationary. The value of $\mu$ is ______ (take $g = 10\ \text{m/s}^2$)
Answer: (B) $0.67$
Work in the cube's frame, where each block feels a pseudo-force $ma = m\dfrac{g}{2} = 5m$ N towards the left.
Block $P$ (smooth top): the only horizontal forces are the pseudo-force ($10$ N, left) and the tension (right), so $T = 10$ N.
Block $Q$ (on the right face): the pseudo-force $1.5 \times 5 = 7.5$ N presses it against the face, so $N = 7.5$ N. Vertically, weight $15$ N down, tension $10$ N up; friction must supply the remaining $5$ N upward:
$$\mu N \ge 5 \;\Rightarrow\; \mu \ge \frac{5}{7.5} = 0.67$$
Solution by Sreeraj P, M.Sc Physics