$A$ steel ring of radius $r$ and cross-section area $A$ is fitted onto a wooden disc of radius $R$ $(R > r)$. If Young's modulus is $E$,then the force with which the steel ring is expanded is:

Two tuning forks $A$ and $B$ produce $8\ Hz$ beats per second when sounded together. $A$ gas column $37.5\ cm$ long in a pipe closed at one end resonates in its fundamental mode with fork $A$,whereas a column of length $38.5\ cm$ of the same gas in a similar pipe is required for a similar resonance with fork $B$. The frequencies of these two tuning forks are:

In the isoelectronic series of metal carbonyls,the $CO$ bond strength is expected to increase in the order:

Sodium and copper have work functions $2.3 \ eV$ and $4.5 \ eV$ respectively. The ratio of the threshold wavelength of sodium to that of copper is nearest to:

The r.m.s. velocity of $CO_2$ at a temperature $T$ (in kelvin) is $x \ cm \ s^{-1}$. At what temperature (in kelvin),the r.m.s. velocity of nitrous oxide would be $4 x \ cm \ s^{-1}$ (in $T$)? (Atomic weights of $C, N$ and $O$ are respectively $12, 14$ and $16$)

$A$ uniform chain of length $L$ is lying on a horizontal table. If the coefficient of friction between the chain and the table top is $\mu$, what is the maximum length of the chain that can hang over the edge of the table without disturbing the rest of the chain on the table?