## Question

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?

### Solution

*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

Now,

Gives,

#### SIMILAR QUESTIONS

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 2*r* 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 *P _{0}*denotes 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 4*a*?

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 *v _{r}*. What will be the terminal velocity of a brass sphere of radius 2

*r*falling 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