Mechanics - Physics Previous Year Questions

Consider that $\sigma_s, k_B, b$ represents Stefan-Boltzmann constant, Boltzmann constant and Wien's displacement law constant, respectively. The dimension of $\sigma_s k_B^{-1} b$ is

A particle of mass $M$ moves along a horizontal $x$ axis from $x=0$ to $x=L$. The coefficient of kinetic friction varies as a function of $x$ as $\mu_k(x)=\mu_0-\alpha x$, where $\mu_0$, $\alpha$ are constants of appropriate dimensions, so that $\mu_k(L)=0$. The total work done by the frictional force during the motion is $n \mu_0 M g L$, where $g$ is the acceleration due to gravity. The value of $n$ is:

A car travels on a circular racetrack of radius 50 m , which is banked at an angle $\theta$. If the car travels at a speed $10 \mathrm{~ms}^{-1}$, then the wear and tear on its tyres is minimum. Taking the acceleration due to gravity to be $10 \mathrm{~ms}^{-2}$, the value of $\theta$ is:

A frictionless circular wire of unit radius is fixed on the horizontal plane. Two-point particles of unit mass start moving simultaneously from point $A\left(\theta=\frac{\pi}{2}\right)$ with identical uniform angular speeds in opposite directions, and meet again at point $B\left(\theta=-\frac{\pi}{2}\right)$. During this time, which of the following figures schematically represent the magnitude of the total linear momentum $P$ of the system, as a function of $\theta$ ?