A horizontal pipe carries water in a streamlined flow. At a point along the pipe, where the cross-sectional area is $10 \mathrm{~cm}^{-2}$, the velocity of water is $1 \mathrm{~ms}^{-1}$ and the pressure is 2000 Pa . What is the pressure of water at another point where the cross-sectional area is $5 \mathrm{~cm}^2$ ?

[Density of water $=1000 \mathrm{kgm}^{-3}$ ]

While determining the coefficient of viscosity of the given liquid, a spherical steel ball sinks by a distance $\mathrm{h}=0.9 \mathrm{~m}$. The radius of the ball $\mathrm{r}=\sqrt{3} \times 10^{-3} \mathrm{~m}$. The time taken by the ball to sink in three trails are tabulated as follows.

$$ \begin{array}{|l|l|} \hline \text { Trial No. } & \text { Time taken by the ball to fall by } \mathrm{h} \text { (in second) } \\ \hline 1 . & 2.75 \\ \hline 2 . & 2.65 \\ \hline 3 . & 2.70 \\ \hline \end{array} $$

The difference between the densities of the steel ball and the liquid is $7000 \mathrm{~kg} \mathrm{~m}^{-3}$. If $\mathrm{g}=10 \mathrm{~ms}^{-2}$, then the coefficient of viscosity of the given liquid at room temperature is

Water flows through a horizontal pipe of varying cross-section at a rate of $0.314 \mathrm{~m}^3 \mathrm{~s}^{-1}$. The velocity of water at a point where the radius of the pipe is 10 cm is

A closed water tank has cross-sectional area $$A$$. It has a small hole at a depth of $$h$$ from the free surface of water. The radius of the hole is $$r$$ so that $$r \ll \sqrt{\frac{A}{\pi}}$$. If $$p_o$$ is the pressure inside the tank above water level and $$p_a$$ is the atmospheric pressure, the rate of flow of the water coming out of the hole is ( $$\rho$$ is density of water)

Two capillary tubes $$P$$ and $$Q$$ are dipped vertically in water. The height of water level in capillary tube $$P$$ is $$\frac{2}{3}$$ of the height in capillary tube $$Q$$. The ratio of their diameter is

Iceberg floats in water with part of it submerged. What is the fraction of the volume of iceberg submerged, if the density of ice is $$\rho_i=0.917 \mathrm{~g} \mathrm{~cm}^{-3}$$ ?

A cylindrical container containing water has a small hole at height of $$H=8 \mathrm{~cm}$$ from the bottom and at a depth of $$2 \mathrm{~cm}$$ from the top surface of the liquid. The maximum horizontal distance travelled by the water before it hits the ground $$x$$ is

An aluminium sphere is dipped into water. Which of the following is true?