Two identical discs of same radius R are rotating about their axes in opposite directions with the same constant angular speed $$\omega $$. The discs are in the same horizontal plane. At time t = 0, the points P and Q are facing each other as shown in the figure. The relative speed between the two points P and Q is v_r. In one time period (T) of rotation of the discs, v_r as a function of time is best represented by

Six point charges are kept at the vertices of a regular hexagon of side $$L$$ and center $$O,$$ as shown in the figure. Given that $$K = {1 \over {4\pi {\varepsilon _0}}}{q \over {{L^2}}},$$ which of the following statement(s) is (are) correct ?

In the given circuit, a charge of $$+80$$ $$\mu C$$ is given to the upper plate of the $$4$$ $$\mu F$$ capacitor. Then in the steady state, the charge on the upper plate of the $$3$$ $$\mu F$$ capacitor is

A student is performing the experiment of resonance Column. The diameter of the column tube is 4 cm. The frequency of the tuning fork is 512 Hz. The air temperature is 38^oC in which the speed of sound is 336 m/s. The zero of the meter scale coincides with the top end of the Resonance Column tube. When the first resonance occurs, the reading of the water level in the column is