A small bar starts sliding down on inclined plane forming an angle $\theta $ with the horizontal. The friction coefficient depends on the distance $x$ covered as $\mu = kx$ , where $k$ is a constant. Find the distance covered by the bar till it stops
$\frac{{\tan \,\theta }}{k}$
$\frac{2\,{\tan \,\theta }}{k}$
$\frac{3\,{\tan \,\theta }}{k}$
None
A ball is thrown vertically downwards from a height of $20\, m$ with an initial velocity $v_0$, It collides with the ground, loses $50$ percent of its energy in collision and rebounds same height. The initial velocity $v_0$ .................... $\mathrm{ms}^{-2}$ (Take $g=10 \,ms^{-2}$)
A particle which is experiencing a force, given by $\vec F = 3\vec i -12\vec j$, undergoes a displacement of $\vec d = 4\vec i$ . If the particle had a kinetic energy of $3\, J$ at the beginning of the displacement, what is its kinetic energy at the end of the displacement?
A uniform chain of mass $m$ and length $L$ is originally placed mid-way on the top of a fixed smooth double-sided wedge (Figure- $A$). The length of each side of the wedge is $L$ . It is then given a slight push. The kinetic energy of the chain when the whole chain has just slid to the left side of the wedge (Figure- $B$), is :
A body of mass $0.5\; kg$ travels in a stratght line with velocity $v=a x^{3 / 2}$ where $a=5\; m ^{-1 / 2} s ^{-1}$ What is the work done (in $J$) by the net force during its displacement from $x=0$ to $x=2\; m ?$
A block of mass $10\, kg,$ moving in $x$ direction with a constant speed of $10\, m s^{-1}$, is subjected to a retarding force $F= 0.1\,x \,J/m$ during its travel from $x = 20 \,m $ to $30\, m$. Its final $KE$ will be ............... $\mathrm{J}$