Mechanical Prop...

A small spherical drop fall from rest in viscous liquid. Due to friction, heat is produced. The correct relation between the rate of production of heat and the radius of the spherical drop at terminal velocity will be

When one end of the capillary is dipped in water, the height of water column is $$'h'$$. The upward force of $$105$$ dyne due to surface tension balanced by the force due to the weight of water column. The inner circumference of the capillary is
(Surface tension of water $$= 7\times 10^{-2}N/m)$$

A tank is filled with water of density 1 g $$cm^{-3}$$ and oil of density 0.9 g $$cm^{-3}$$. The height of water layer is 100 cm and of the oil layer is 400 cm. If g = 980 cm $$s^{-2}$$, then the velocity of efflux from an opening in the bottom of the tank is :

The potential energy of a molecules on the surface of a liquid compared to the one inside the liquid is :

A sphere of radius R and density $$\rho_1$$ is dropped in a liquid of density $$\sigma$$. Its terminal velocity is $$v_1$$. If another sphere of radius R and density $$\rho_2$$ is dropped in the same liquid, its terminal velocity will be

A capillary tube of radius $$r$$ is immersed in water and water rises in it to a height $$h$$. Mass of water in the capillary tube is $$m$$. If the radius of the tube is doubled, mass of water that will rise in the capillary tube will now be

Two spherical rain drops with radii in the ratio $$1:2$$ fall from a great height through the atmosphere. The ratio of their momenta after they have attained terminal velocity is

Equal volume of two immiscible liquids of densities $$\rho$$ and $$2\rho$$ are filled in a vessel as shown in figure. Two small holes are made at depth $$\dfrac {h}{2}$$ and $$\dfrac {3h}{2}$$ from the surface of lighter liquid. If $$v_{1}$$ and $$v_{2}$$ are the velocities of efflux at these two holes, then $$\dfrac{v_{1}}{v_{2}}$$ will be

A large tank is filled with water to a height H. A small hole is made at the base of the tank. It takes 71 time to decrease the height of water to $$\frac {H}{\eta }(\eta > 1)$$ and $$T_2$$ time to take out the rest of 11 water. If $$T_1 = T_2$$ then the value of $$\eta$$ is 

A cylindrical tank has a hole of $$1$$ $$cm^2$$ m bottom. If the water is allowed to flow into the tank from a tube above it at the rate of $$70cm^2/s$$, then the maximum height up to which water can rise in the tank is?