An a.c. voltage source $\mathrm{V}=\mathrm{V}_0 \sin \omega \mathrm{t}$ is connected across resistance ' $R$ ' and capacitance ' $C$ ' in series. It is given that $R=\frac{1}{\omega c}$ and the peak current is $\mathrm{I}_0$. If the angular frequency of the voltage source is changed to $\left(\frac{\omega}{\sqrt{3}}\right)$, then the new peak current in the circuit is

The black discs $\mathrm{x}, \mathrm{y}$ and z have radii $1 \mathrm{~m}, 2 \mathrm{~m}$ and 3 m respectively. The wavelengths corresponding to maximum intensity are $200 \mathrm{~nm}, 300 \mathrm{~nm}$ and 400 nm respectively. The relation between emissive power $E_x, E_y$ and $E_z$ is

The height ' h ' from the surface of the earth at which the value of ' $g$ ' will be reduced by $64 \%$ than the value at surface of the earth is ( $\mathrm{R}=$ radius of the earth)

The length of a sonometer wire 'AB' is 110 cm . Where should the two bridges be placed from end ' $A$ ' to divide the wire in three segments whose fundamental frequencies are in the ratio $1: 2: 3$ ?