Curved surface of a vessel has shape of truncated cone having semi vertex angle ${37}^{\mathrm{o}}$ . Vessel is full of water (density $\mathrm{\rho }=1000 \mathrm{kg} {\mathrm{m}}^{-3}$ ) upto a height of $13 \mathrm{cm}$ and is placed on a smooth horizontal plane. Upper surface is opened to atmosphere. A hole of $1.5\mathrm{ }\mathrm{c}{\mathrm{m}}^2$ is made on curved wall at a height of $8 \mathrm{cm}$ from bottom as shown in figure. Area of water surface in the vessel is large as compared to the area of hole.

(Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The platelets are drifting with the blood flowing in a streamline flow through a horizontal artery as shown below:

Artery is contracted in region $\mathrm{II}$. Choose the correct statement.

What will be the nature of flow of water from a circular tap, when its flow rate increased from $0.18 \mathrm{L} {\left(\min \right)}^{-1}$ to $0.48 \mathrm{L} {\left(\min \right)}^{-1}?$ The radius of the tap and viscosity of water are $0.5 \mathrm{cm}$ and ${10}^{-3} \mathrm{Pa} \mathrm{s}$, respectively. (Density of water : ${10}^3 \mathrm{kg} {\mathrm{m}}^{-3}$)

Consider the configuration of a stationary water tank of cross-section area $A_0$ and a small bucket as shown in figure below;

What should be the speed $v$ of the bucket, so that the water leaking out of a hole of cross-section area $A$ (as shown) from the water tank does not fall outside the bucket?

(Take, $h=5 \mathrm{m}, H=5 \mathrm{m}, \mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}, A=5 {\mathrm{cm}}^2$ and $A_0=500 {\mathrm{cm}}^2$).