A spherical solid ball of volume $V$ is made of a material of density ${\rho _1}$ . It is falling through a liquid of density ${\rho _2}\left( {{\rho _2} < {\rho _1}} \right)$. Assume that the liquid applies a viscous force on the ball that is propoertional to the square of its speed $v$ , i.e., ${F_{{\rm{viscous}}}} = - k{v^2}\left( {k > 0} \right)$. Then terminal speed of the bal is

- A
$\sqrt {\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}} $

- B
$\frac{{Vg{\rho _1}}}{k}$

- C
$\sqrt {\frac{{Vg{\rho _1}}}{k}} $

- D
$\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}$

Horizontal tube of non-uniform cross-section has radius of $0.2\,m$ and $0.1\,m$ respectively at $P$ and $Q$. For streamline flow of liquid, the rate of liquid flow

Consider a water jar of radius $R$ that has water filled up to height $H$ and is kept on a stand of height $h$ (see figure). Through a hole of radius $r(r < < R)$ at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is $x$. Then

A wind with speed $40\,m/s$ blows parallel to the roof of a house. The area of the roof is $250\,m^2.$ Assuming that the pressure inside the house is atmospheric pressure, the force exerted by the wind on the roof and the direction of the force will be $(\rho _{air} = 1.2\,kg/m^3)$

A cylindrical vessel filled with water upto the height $H$ becomes empty in time $t_0$ due to a small hole at the bottom of the vessel. If water is filled to a height $4H$ it will flow out in time

A wooden block with a coin placed on its top floats in water as shown in figure. $l$ and $h$ are as shown. After some time the coin falls into the water then