A small metal sphere of density $\rho$ is dropped from height $h$ into a jar containing liquid of density $\sigma(\sigma>\rho)$. The maximum depth up to which the sphere sinks is (Neglect damping forces)

A composite slab consists of two materials having coefficients of thermal conductivity K and $2 K$, thickness $x$ and $4 x$ respectively. The temperatures of two outer surfaces of a composite slab are $\mathrm{T}_2$ and $\mathrm{T}_1$ respectively $\left(\mathrm{T}_2>\mathrm{T}_1\right)$. The rate of heat transfer through the slab in a steady state is $\left[\frac{A\left(T_2-T_1\right) K}{x}\right] f$, where $f$ is equal to

In an organ pipe closed at one end; the sum of the frequencies of first three overtones is 3930 Hz . The frequency of the fundamental mode of organ pipe is

A uniformly charged conducting sphere of diameter 3.5 cm has a surface charge density of $20 \mu \mathrm{Cm}^{-2}$. The total electric flux leaving the surface of the sphere is nearly [permittivity of free space, $\varepsilon_0=8.85 \times 10^{-12} \mathrm{SI}$ unit]