A solid cylinder of length $l$ and cross-sectional area $\frac{a}{5}$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $l / 4$ in the denser liquid as shown in figure. The lower density liquid ( $\rho$ ) is open to atmosphere having pressure $\mathrm{P}_0$. The density d of solid cylinder is

The amount of work done in blowing a soap bubble such that its diameter increases from $\mathrm{d}_1$ to $\mathrm{d}_2$ is ( $\mathrm{T}=$ surface tension of soap solution)

The energy needed for breaking a liquid drop of radius ' $R$ ' into 216 droplets, each of radius ' $r$ ' is ' $x$ ' times $T R^2$. The value of ' $x$ ' is [ $T=$ surface tension of the liquid].

The excess pressure inside first soap bubble is three times that of a second soap bubble. The ratio of volumes of the first to second bubble