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
The net downward force acting on the bob is
This is the effective acceleration due to gravity.
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
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?
A wooden block of mass m and density is tied to a string; the other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density . What is the tension in the string.