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

When a ceiling fan is switched off, its angular velocity falls to $\left(\frac{1}{3}\right)^{\text {rd }}$ while it makes 24 rotations. How many more rotations will it make before coming to rest?

In Young's double slit interference experiment, using two coherent sources of different amplitudes, the intensity ratio between bright to dark fringes is $5: 1$. The value of the ratio of resultant amplitudes of bright fringe to dark fringe is

One end of a capillary tube is dipped in water, the rise of water column is ' $h$ '. The upward force of 98 dyne due to surface tension is balanced by the force due to the weight of the water column. The inner circumference of the capillary is $\left(\right.$ surface tension of water $\left.=7 \times 10^{-2} \mathrm{Nm}^{-1}\right)$