A string of mass $0.1 \mathrm{kgm}^{-1}$ has length 0.9 m . It is fixed at both ends and stretched such that it has a tension of 40 N . The string vibrates in three segments with amplitude 0.3 cm . The amplitude (maximum) of the particle velocity is (in $\mathrm{m} / \mathrm{s}$)

A thin uniform rod of mass ' $m$ ' and length ' $L$ ' is pivoted at one end so that it can rotate in a vertical plane. The free end is held vertically above pivot and then released. The angular acceleration of the rod when it makes an angle ' $\theta$ ' with the vertical is [consider negligible friction at the pivot] ( $\mathrm{g}=$ acceleration due to gravity)

The molar specific heat of an ideal gas at constant pressure and constant volume is ' $\mathrm{C}_{\mathrm{p}}$ ' and ' $\mathrm{C}_{\mathrm{v}}$ ' respectively. If ' R ' is a universal gas constant and the ratio of ' $\mathrm{C}_{\mathrm{p}}$ ' to ' $\mathrm{C}_{\mathrm{v}}$ ' is $\gamma$, then ' $\mathrm{C}_{\mathrm{p}}$ ' is equal to

Two charges $\mathrm{q}_1=+6_{\mathrm{q}}$ and $\mathrm{q}_2=-3 \mathrm{q}$ placed as shown in figure. A proton is placed on x -axis away from $\mathrm{q}_2$. To remain proton in equilibrium, the distance between $\mathrm{q}_1$ and proton is