$A$ $4 \, kg$ mass and a $1 \, kg$ mass are moving with equal kinetic energies. The ratio of the magnitudes of their linear momenta is

The electronic configuration of $Yb^{2+}$ is:

If $\sin ^{-1} x - \cos ^{-1} x = \frac{\pi}{6}$,then $x$ is equal to

Two particles $P$ and $Q$ start from the origin and execute Simple Harmonic Motion along the $X$-axis with the same amplitude but with periods $3 \ s$ and $6 \ s$ respectively. The ratio of the velocities of $P$ and $Q$ when they meet is

In a compound,$C, H,$ and $N$ atoms are present in the ratio $9 : 1 : 3.5$ by weight. If the molecular weight of the compound is $108$,what is its molecular formula?

$A$ spherically symmetric gravitational system of particles has a mass density $\rho = \begin{cases} \rho_0 & \text{for } r \leq R \\ 0 & \text{for } r > R \end{cases}$ where $\rho_0$ is a constant. $A$ test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed $V$ as a function of distance $r$ $(0 < r < \infty)$ from the centre of the system is represented by: