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

Two capacitors of $100 \mu \mathrm{~F}$ and $50 \mu \mathrm{~F}$ are connected in parallel. If the potential difference across $100 \mu \mathrm{~F}$ is 20 V and across $50 \mu \mathrm{~F}$ is 40 V , then the common potential of the parallel combination will be (same polarities of the capacitor connected together)

$\mathrm{I}-\mathrm{V}$ characteristics of LED is shown correctly by graph

What is the linear velocity if angular velocity $\vec{\omega}=3 \hat{i}-4 \hat{j}+\hat{k}$ and radius $\vec{r}=(5 \hat{i}-6 \hat{j}+6 \hat{k})$ ?