If the potential at the centre of a uniformly charged ring is $V_0$,then the electric field at its centre will be (assume radius $= R$):

The time constant of an inductance coil is $3 \text{ ms}$. When a $90 \Omega$ resistance is joined in series,the time constant becomes $0.5 \text{ ms}$. The inductance and the resistance of the coil are:

An $X$-ray tube produces a continuous spectrum of radiation with its shortest wavelength of $45 \times 10^{-2} \text{ \AA}$. The maximum energy of a photon in the radiation in $eV$ is $(h = 6.62 \times 10^{-34} \text{ J-s}, c = 3 \times 10^8 \text{ m/s})$. (in $27,500$)

$A$ metal crystallises in a face-centred cubic $(FCC)$ structure. If the edge length of its unit cell is $a$,the closest approach between two atoms in the metallic crystal will be:

The number of structural isomers for $C_6H_{14}$ is

$A$ bullet fired into a fixed target loses half of its velocity after penetrating $3\, cm$. How much further will it penetrate before coming to rest,assuming that it faces constant resistance to motion?.......$cm$