The length of a potentiometer wire is ' $L$ '. A cell of e.m.f. ' $E$ ' is balanced at a length $\frac{L}{4}$ from the positive end of the wire. If the length of the original wire is increased by $\frac{\mathrm{L}}{3}$, then using the same cell null point is obtained at

An open organ pipe is closed such that the third overtone of the closed pipe is found to be higher in frequency by 200 Hz than the second overtone of the original pipe. The fundamental frequency of the open pipe is (Neglect end correction)

Same current is flowing in two different a.c. circuits. First circuit contains only inductance and second contains only capacitance. If the frequency of a.c. is increased in both circuits, the current will

A particle is executing S.H.M. of amplitude ' $A$ '. When the potential energy of the particle is half of its maximum value during the oscillation, its displacement from the equilibrium position is