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:

The power of a crane, which lifts a mass of 1000 kg to a height of 20 m in 10 s is: $\left(g=9.8 \mathrm{~m} / \mathrm{s}^2\right)$

The kinetic energies of two similar cars $A$ and $B$ are 100 J and 225 J respectively. On applying breaks, car $A$ stops after 1000 m and car $B$ stops after 1500 m . If $F_A$ and $F_B$ are the forces applied by the breaks on cars $A$ and $B$ respectively, then the ratio of $\frac{F_A}{F_B}$ is

A bob of heavy mass $m$ is suspended by a light string of length $/$. The bob is given a horizontal velocity $v_0$ as shown in figure. If the string gets slack at some point $P$ making an angle $\theta$ from the horizontal, the ratio of the speed $v$ of the bob at point $P$ to its initial speed $v_0$ is: