The radius of gyration of a disc of mass $50\,g$ and radius $2.5\,cm$,about an axis passing through its centre of gravity and perpendicular to the plane,is ....... $cm$.

If $\log (1+x) - \frac{2x}{2+x}$ is increasing, then

The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension,when the same tension is applied?

Two identical vessels $A$ and $B$ with frictionless pistons contain the same ideal gas at the same temperature and the same volume $V$. The masses of gas in $A$ and $B$ are $m_A$ and $m_B$,respectively. The gases are allowed to expand isothermally to the same final volume $2V$. The changes in pressures of the gas in $A$ and $B$ are found to be $\Delta P$ and $1.5 \Delta P$,respectively. Then:

If the pairs of straight lines $x^2-2 p x y-y^2=0$ and $x^2-2 q x y-y^2=0$ are such that each pair bisects the angle between the other pair,then

The first line in the Lyman series has wavelength $\lambda$. The wavelength of the first line in the Balmer series is