Three equal charges are placed on the three corners of a square as shown below. If the magnitude of force between ' $\mathrm{q}_1$ ' and ' $\mathrm{q}_2$ ' is ' $\mathrm{F}_{12}$ ' and that between ' $\mathrm{q}_1$ ' and ' $\mathrm{q}_3$ ' is $\mathrm{F}_{13}$, then the ratio of $F_{13}$ to $F_{12}$ is

Two bodies of mass 10 kg and 5 kg are moving in concentric circular orbits of radii ' R ' and ' r ' respectively such that their periods are same. The ratio between their centripetal acceleration is

Two moles of an ideal monoatomic gas undergo a cyclic process as shown in figure. The temperatures in different states are given as $6 \mathrm{~T}_1=3 \mathrm{~T}_2=2 \mathrm{~T}_4=\mathrm{T}_3=2400 \mathrm{~K}$. The work done by the gas during the complete cycle is ( $\mathrm{R}=$ Universal gas constant)

The amplitude of a damped oscillator becomes $\left(\frac{1}{3}\right)^{\mathrm{rd}}$ of original amplitude in 2 seconds. If its amplitude after 6 second become $\left(\frac{1}{n}\right)$ times the original amplitude, the value of $n$ is ( $n$ is non zero integer)