Let $y=y(x)$ be the solution of the differential equation $\left(x^2-x \sqrt{x^2-1}\right) d y+\left(y\left(x-\sqrt{x^2-1}\right)-x\right) d x=0, x \geq 1$. If $y(1)=1$, then the greatest integer less than $y(\sqrt{5})$ is $\_\_\_\_$ .

The density $\rho$ of a uniform cylinder is determined by measuring its mass $m$, length $l$ and diameter $d$. The measured values of $m, l$ and $d$ are $97.42 \pm 0.02 \mathrm{~g}$, $8.35 \pm 0.05 \mathrm{~mm}$ and $20.20 \pm 0.02 \mathrm{~mm}$, respectively. Calculated percentage fractional error in $\rho$ is $\_\_\_\_$ .

The potential energy of a particle changes with distance $x$ from a fixed origin as $V=\frac{A \sqrt{x}}{x+B}$, where $A$ and $B$ are constant with appropriate dimensions. The dimensions of $A B$ are $\_\_\_\_$

The rain drop of mass 1 g , starts with zero velocity from a height of 1 km . It hits the ground with a speed of $5 \mathrm{~m} / \mathrm{s}$. The work done by the unknown resistive force is $\_\_\_\_$ J.

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