$A$ ball is thrown on a lawn in such a way that it initially slides with a speed $v_0$ without rolling. It gradually picks up rotational motion. Find the speed of the ball at which there will be rolling without slipping.

If a gas contains only three molecules that move with velocities of $100, 200, 500 \ ms^{-1}$. What is the $rms$ velocity of that gas in $ms^{-1}$?

Consider the following reaction equilibrium:
$N_{2(g)} + 3H_{2(g)} \rightleftharpoons 2NH_{3(g)}$
Initially,$1 \text{ mole}$ of $N_2$ and $3 \text{ moles}$ of $H_2$ are taken in a $2 \text{ L}$ flask. At equilibrium state,if the number of moles of $N_2$ is $0.6$,what is the total number of moles of all gases present in the flask?

The wavelengths of electron waves in two orbits is $3: 5$. The ratio of kinetic energy of electrons will be

$A$ $0.001 \, \text{molal}$ solution of $[Pt(NH_3)_4Cl_4]$ in water shows a freezing point depression of $0.0054 \, ^\circ C$. If $K_f$ for water is $1.80$,the correct formulation of the above compound is?

The voltage of an $ac$ source varies with time according to the equation $V = 100 \sin(100 \pi t) \cos(100 \pi t)$,where $t$ is in seconds and $V$ is in volts. Then: