A ball collides perfectly inelastically with smooth horizontal ground at angle $30°$ with vertical as shown. Fraction of kinetic energy lost by the ball due to collision is _____

A rod of mass $10 \mathrm{kg}$ and length $2 \mathrm{m}$ is lying on a horizontal table. The minimum work done in $\mathrm{J}$ making it stand on one end will be _____.

(Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

By applying a force $\overrightarrow{F}=\left(3xy-5z\right)\hat{j}+4z\hat{k}$ a particle is moved along the path $y=x^2$, where all quantities are in $SI$ units, from point $(0,0,0) m$ to the point $(2,4,0)\mathrm{m}$. The work done by force $\overrightarrow{F}$ on the particle (in joule), is _____.

A particle of mass $m$ moving with a speed $u$ strikes a smooth horizontal surface at an angle $45°$. The particle rebounds at an angle $\mathrm{\varphi }$ with speed$v$. If coefficient of restitution is  $\frac{1}{\sqrt{3}}$, then angle $\mathrm{\varphi }$ is