Two circular loops $P$ and $Q$ of radii $r$ and $nr$ respectively are made from a uniform wire. The moment of inertia of $Q$ about its axis is four times that of $P$ about its axis. The value of $n$ is

The magnetic field $(B)$ inside a long solenoid having $n$ turns per unit length and carrying current $I$ when an iron core is kept in it is ($\mu_0 = $ permeability of vacuum,$\chi = $ magnetic susceptibility).

$A$ string of length $L$ is fixed at one end and carries a mass $M$ at the other end. The string makes $2/\pi$ revolutions per second around the vertical axis through the fixed end as shown in the figure,then the tension in the string is:

An auditorium has a volume of $10^5 \ m^3$ and a total absorption area of $2 \times 10^4 \ m^2$. Its average absorption coefficient is $0.2$. The reverberation time of the auditorium in seconds is:

$A$ compound absorbs light in the wavelength region $490-500 \ nm$. Its complementary colour is