A small sphere of radius r falls from rest in a viscous liquid. As a result, heat is produced due to the viscous force. The rate of production of heat when the sphere attains its terminal velocity is proportional to

A small hole of an area of cross-section 2 $m{m}^2$ is present near the bottom of a fully filled open tank of height 2 m. Taking g= 10 $m/s^2$, the rate of flow of water through the open hole would be nearly:

A soap bubble, having a radius of 1 mm, is blown from a detergent solution having a surface tension of $2.5\times {10}^{-2}N/m$. The pressure inside the bubble equals at a point $Z_0$ below the free surface of the water in a container. Taking g= 10 m/$s^2$, density of water = ${10}^{3}kg/m^3$, the value of $Z_0$ is:

The density of ice is x gm/cc and that of water is y gm/cc. What is the change in volume in cc, when m gm of ice melts?

A body weighs 160 g in air, 130 g in water and 136 g in oil. The specific gravity of oil is

Three liquids of densities d, 2d and 3d are mixed in equal proportions of weights. The relative density of the mixture is:

By sucking through a straw, a student can reduce the pressure in his lungs to 750 mm of Hg $(\mathrm{density} = 13.6 \mathrm{gm}/{\mathrm{cm}}^3).$ Using the straw, he can drink water from a glass up to a maximum depth of :

If the terminal speed of a sphere of gold $(\mathrm{density} = 19.5 \mathrm{kg}/{\mathrm{m}}^3)$ is 0.2 m/s in a viscous liquid $(\mathrm{density} = 1.5 \mathrm{kg}/{\mathrm{m}}^3),$ find the terminal speed of a sphere of silver $(\mathrm{density} = 10.5 \mathrm{kg}/{\mathrm{m}}^3)$ of the same size in the same liquid

$1 {\mathrm{m}}^3$ water is brought inside the lake up to 200 metres depth from the surface of the lake. What will be changed in the volume when the bulk modulus of elastically of water is 22000 atmosphere? 
$(\mathrm{density} \mathrm{of} \mathrm{water} \mathrm{is} 1 \times {10}^3 \mathrm{kg}/{\mathrm{m}}^3 \mathrm{atmosphere} \mathrm{pressure} = {10}^{5 }\mathrm{N}/{\mathrm{m}}^2 \mathrm{and} \mathrm{g} = 10 \mathrm{m}/{\mathrm{s}}^2 )$

Two horizontal pipes have radii in ratio 1 : 2 and
lengths in ratio 1 : 2. Same viscous fluid flows at
same pressure difference in both the pipes. The flow
rates are in the ratio

An ice block of volume $\frac{32\mathrm{\pi }}{3}c{m}^3$is placed in
gravity free space. When ice completely melts, then
its surface area - (Neglect difference in density of ice and water)

Two small spherical metal balls, having equal masses, are made from materials of densities ${\rho }_1 and {\rho }_2$ such that ${\rho }_1=8{\rho }_2$ and having radii of 1 mm and 2 mm, respectively. They are made to fall vertically (from rest) in a viscous medium whose coefficient of viscosity equals $\eta$ and whose density is 0.1${\rho }_2$. The ratio of their terminal velocities would be:

In a U-tube, as shown in the figure, the water and oil are in the left side and right side of the tube respectively. The height  for water and oil columns are 15 cm and 20 cm respectively. The density of the oil is: $[take {\rho }_{water}=1000 kg/m^3]$

The surface tension of the soap solution is $2 \mathrm{x} {10}^{-2}$ N/m. If a soap bubble of radii 4 cm is blown, then the amount of work done is:

A small tiny water droplet is falling towards earth at a uniform speed of 1 cm/s. When 27 such identical droplets combine together to form a bigger drop, then with what uniform velocity will this bigger drop fall?

The velocity of water in a river is

A steel ball is dropped on the water surface from zero height. The variation of the viscous force with time on the ball can be represented as

A body with an air cavity loses one-third of weight when immersed in water. If the relative density of the material of the body is 6, then the ratio of the volume of the cavity to the volume of the body is:

Which of the following graphs correctly shows the variation in kinetic energy (KE) of a metal sphere falling freely in a lake? Assume sufficient depth of the lake to impart terminal velocity to the sphere (d: depth)