A vehicle runs on a straight road of length 'L'. It travels half the distance with speed V and the remaining distance with speed $\frac{\mathrm{V}}{3}$. Its average speed is

A particle of mass ' $m$ ' performs uniform circular motion of radius ' $r$ ' with linear speed ' $v$ ' under the application of force ' $F$ '. If ' $m$ ', ' $v$ ' and $' \mathrm{r}$ ' are all increased by $20 \%$ the necessary change in force required to maintain the particle in uniform circular motion, is

In Young's double slit experiment, the distance between the two coherent sources is ' d ' and the distance between the source and screen is ' D '. When the wavelength $(\lambda)$ of light source used is $\frac{d^2}{3 D}$, then $n^{\text {th }}$ dark fringe is observed on the screen, exactly in front of one of the slits. The value of ' $n$ ' is

A particle starts oscillating simple harmonically from its equilibrium position with time period ' T '. What is the ratio of potential energy to kinetic energy of the particle at time $t=\frac{T}{12}$ ? $$\left(\sin \left(\frac{\pi}{6}\right)=\frac{1}{2}\right)$$