A cylinder has a radius r. To what height h should it be filled with water so that the thrust on its walls is equal to that on its bottom?
h = r
If is the density of water, pressure p due to height h is
Now, area of the base . Therefore, thrust at the bottom is
Pressure p also acts on the wall. The average pressure on the wall . Surface area of wall up to . Therefore, thrust on the walls is
The work done to break up a drop of a liquid of radius R and surface tension into eight drops, all of the same size, is
A soap bubble of radius r is blown up to form a bubble of radius 2r under isothermal conditions. If is the surface tension of soap solution, the energy spent in doing so is
If the air bubble is formed at a depth h inside the container of soap solution of density , the total pressure inside the bubble is (here P0denotes the atmospheric pressure)
A small drop of water of surface tension is squeezed between two clean glass plates so that a thin layer of thickness d and area A is formed between them. If the angle of contact is zero, the force required to pull the plates apart is
Eight drop of water, each of radius r, coalesce to form a single big drop. The energy released is used up in raising the temperature of the big drop. If is the surface tension of water and its density and J the mechanical equivalent of heat (all expressed in SI units), the rise in the temperature of the drop is
Water rises to a height h in a capillary tube of area of cross-section a. To what height will water rise in a capillary tube of area of cross-section 4a?
A metal sphere of volume V, having a cavity inside it, floats on water completely submerged. If the relative density of the metal is 1.5, the volume of the cavity is
The terminal velocity of a tiny brass sphere of radius r falling in a viscous liquid is vr. What will be the terminal velocity of a brass sphere of radius 2rfalling in the same liquid.
A spherical small ball of density is gently released in a liquid of density . The initial acceleration of the free fall of the ball will be
The time period of a simple pendulum is T. The pendulum is oscillated with its bob immersed in a liquid of density . If the density of the bob is and viscous effect is neglected, the time period of the pendulum will be