Mechanical Prop...

A boat travelling at $6 m/s$ in sea water has a $250 mm$ diameter propeller that discharges the water at a velocity of $12 m/s$. Given that the density of seawater is $1030 \mathrm{k}\mathrm{g}/\mathrm{m}^{3}$. The effect of propeller hub is negligible. The magnitude of thrust produced $F$ is (in $N$)

A wide vessel with a small hole at the bottom is filled with two liquids. The density and height of one liquid are ${\rho}_{1}\   and\   {h}_{1}$ and that of the other are ${\rho}_{2}$ and ${h}_{2}$. (Given ${\rho}_{1} > {\rho}_{2} )$. The velocity of liquid coming out of the hole is :

The hydraulic press shown in the figure is used to raise the mass $m$ through a height of $0.05 cm$ by performing $500 J$ of work at the small piston. The diameter of the large piston is 10 cm while that of the smaller one is $2 cm.$ The mass $M$ is

Bantu slips into a large lake and he doesn't know swimming. But he is a great fan of Superman. He shouted for help remembering Superman. As usual, Superman arrives on the top of a cliff and, due to some reason, Superman lost his flying power immediately after arrival on cliff. Due to shortage of time, somehow, Superman manages a strong and long straw and decided to drink whole water of lake to save Bantu.(Data:Atmospheric pressure $=1.2 \times 10^{5} Pa, g=10m/s^{2}$, density of water$= 1000kg/m^{3})$ Assume Superman has infinite power and ability to drink whole water. Which of the following statements is/are true?
(1) Superman cannot save Bantu by this way.
(2) Superman can drink some water but not whole water.
(3) Superman will save Bantu by drinking whole water.

The difference in the pressure between the air just over the wing $\mathrm{P}_{1}$ and that under the wing $\mathrm{P}_{2}$  is:

Equal volumes of two immiscible liquids of densities $\delta$ and 3$\delta$ are filled in a vessel. Two small holes are punched at depth $h/3$ and $4h/3$ from upper surface of lighter liquid. If $V_{1}$ and $V_{2}$ are velocities of efflux at these two holes, then $V_{1}/V_{2}$ is :

Water is filled upto height H units in a tank placed on the ground and whose side walls are vertical. A hole is made in one of the vertical wall such that the emerging stream of water strikes the ground at the maximum range. If the level in the tank is changing at the rate of R units per second, at that instant the rate at which range will be changing will be:

A tank is filled up to a height 2H with a liquid and is placed on a platform of height H from the ground. The distance x from the ground where a small hole is punched to get the maximum range R is

A long capillary glass tube of uniform diameter of $1mm$ is filled completely with water and then held vertically in air. It is now opened at both ends. Find the length of the water column remaining in the glass tube. Surface tension of water is $0.075 N/m.$ $(g=10m/s^2$ and density of water is $10^3 kg/m^3)$: