Question
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 $\frac{g}{2}$, where $g$ is gravitational acceleration. During this movement the block P and Q remain stationary. The value of $\mu$ is $\_\_\_\_$。 $\left( \right.\ $ take $\left. \ g = 10\text{ }m/s^{2} \right)$
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Solution
Sol. [Key Concept: Block Q is held on the vertical face by friction while the system accelerates at $\frac{g}{2}$; balance the vertical weight against $\mu\ N$ (with $N$ from the horizontal pseudo-force) to get $\mu$.]
w.r.t bigger block
$${f = \mu N = \mu \times \frac{1.5\text{ }g}{2} }{1.5\text{ }g = g + \mu + \frac{1.5\text{ }g}{2}\ \Rightarrow 0.5 = \mu \times \frac{1.5}{2} }{\left( \mu = \frac{2}{3} \right) }$$
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