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 $\_\_\_\_$ (take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ )

Three masses $m_1=4 \mathrm{~kg}, m_2=4 \mathrm{~kg}$ and $m_3=6 \mathrm{~kg}$ are suspended from a fixed smooth frictionless pully as shown in the figure below. The value of $T_1 / T_2$ is

$\_\_\_\_$

(take $g=10 \mathrm{~m} / \mathrm{s}^2$ )

A wedge $Y$ with mass of 10 kg and all frictionless surfaces and the inclined surface making $37^{\circ}$ with horizontal. A block $X$ with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $t=0$ wedge ( $Y$ ) is pulled toward right with constant force $(f)$ of 24 N . Taking the block $X$ at rest at $t=0$, the time taken by it to slide down 8.8 m on the slope, while $Y$ is on the move, is $\_\_\_\_$ s.

$\left(\right.$ take $\tan \left(37^{\circ}\right)=3 / 4$ and $\left.\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2\right)$

The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is $50 \%$ more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at $45^{\circ}$ with the horizontal. The coefficient of kinetic friction between the rough inclined surface and block is $\_\_\_\_$