The earth is assumed to be a sphere of radius ' $R$ ' and mass ' $M$ ' having period of rotation ' $T$ '. The angular momentum of earth about its axis of rotation is

When a galvanometer is shunted by a resistance ' $S$ ', its current capacity increases ' $n$ ' times. If the same galvanometer is shunted by another resistance $\mathrm{S}^{\prime}$, its current capacity increases to $\mathrm{n}^{\prime}$. The value of $n^{\prime}$ in terms of $n, S$ and $S^{\prime}$ is

In projectile motion two particles of masses $\mathrm{m}_1$ and $m_2$ have velocities $\vec{V}_1$, and $\vec{V}_2$ respectively at time $t=0$. Their velocities become $\overline{V_1^{\prime}}$ and $\overrightarrow{V_2^{\prime}}$ at time 2 t while still moving in air. The value of $\left[\left(m_1 \overrightarrow{V_1^{\prime}}+m_2 \overrightarrow{V_2^{\prime}}\right)-\left(m_1 \vec{V}_1+m_2 \vec{V}_2\right)\right]$ is ( $\mathrm{g}=$ acceleration due to gravity)

The magnetic susceptibility of the material of a rod is 599. The absolute permeability of the material of the rod will be [ $\mu_0=4 \pi \times 10^{-7}$ SI unit]