In a Wheatstone's bridge, the resistances in four arms are as shown in the figure. The balancing condition of the bridge is

Two solid spheres ( A and B ) are made of metals having densities $\rho_A$ and $\rho_B$ respectively. If there masses are equal then ratio of their moments of inertia $\left(\frac{\mathrm{I}_{\mathrm{B}}}{\mathrm{I}_{\mathrm{A}}}\right)$ about their respective diameter is

A stationery wave is represented by $y=12 \cos \left(\frac{\pi}{6} x\right) \sin (8 \pi t)$, where $x \& y$ are in cm and $t$ in second. The distance between two successive antinodes is

A hemispherical portion of radius ' $R$ ' is removed from the bottom of a cylinder of radius ' R '. The volume of the remaining cylinder is ' V ' and its mass is ' M '. It is suspended by a string in a liquid of density ' $\rho$ ', where it stays vertical. The upper surface of the cylinder is at a depth ' $h$ ' below the liquid surface. The force on the bottom of the liquid is