At what temperature will the root mean square speed of ozone $(O_3)$ be equal to the root mean square speed of oxygen $(O_2)$ at $27 \, ^oC$?

$A$ charged particle with charge $q$ and mass $m$ starts with an initial kinetic energy $K$ at the centre of a uniformly charged spherical region of total charge $Q$ and radius $R$. Charges $q$ and $Q$ have opposite signs. The spherically charged region is not free to move and kinetic energy $K$ is just sufficient for the charged particle to reach the boundary of the spherical charge. How much time does it take the particle to reach the boundary of the region?

Dry air is passed through a solution containing $10 \ g$ of solute and $90 \ g$ of water,and then it is passed through pure water. The loss in weight of the solution is $2.5 \ g$ and the loss in weight of the pure solvent is $0.05 \ g$. Calculate the molecular weight of the solute.

The ratio between kinetic and potential energies of a body executing simple harmonic motion,when it is at a distance of $\frac{1}{N}$ of its amplitude from the mean position is

Acetaldehyde forms a white crystalline precipitate on mixing with a ...... solution of

What is the maximum number of rectangular components into which a vector can be split in space?