Laws of Motion question bank (Physics)

A block takes $t$ time to slide down a plane inclined at $45°$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\dfrac{t}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $\left(\dfrac{\alpha}{100}\right)$. The value of $\alpha$ is __________.

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 pulley 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 $g = 10$ m/s$^2$)