A large tank of cross-section area A contains liquid of density `rho` .A cylinder of density `rho/4` ,length `l=40cm` ,and cross-section area a (<

A plank of area of cross-section A is half immersed in liquid 1 of density rho and half in liquid 2 of density 2rho . What is period of osciallation of the plank if it is slightly depressed downwards?

A block of mass m and density p is hanging from a string . If it is lowered into a vessel of cross-sectional area A containing a liquid of density sigma(lt rho) and gets fully immered, the increase in pressure at the bottom of vessel would be

A cylinder of mass m and density rho hanging from a string is lowered into a vessel of cross-section area s containing a liquid of density sigma (lt rho) unit it is fully immersed. The increase in pressure at the bottom of the vessel is

Cylindrical block of area of cross-section A and of material of density rho is placed in a liquid of density one third of density of block. The block compress in the spring is one-third of te length of the block. if acceleration due to gravity is g, the spring constant of the spring is

There are two identical small holes of area of cross section a on the opposite sides of a tank containing liquid of density rho . The differences in height between the holes is h . The tank is resting ona smooth horizontal surface. The horizontal force which will have to be applied on the tank to keep it inequilibrium is

Passage XIV) A uniform cylindrical block of mass 2M and cross-sectional area A remains partially submerged in a non viscous liquid of density rho , density of the material of the cylinder is 3rho . The cylinder is connected to lower end of the tank by means of a light spring of spring constant K. The other end of the cylinder is connected to anotehr block of mass M by means of a light inextensible sting as shown in the figure. The pulleys shown are massless and frictionless and assume that the cross-section of the cylinder is very small in comparison to that of the tank. Under equilibrium conditions, half of the cylinder is submerged. [given that cylinder always remains partially immersed) Under equilibrium conditions

A wide tank of cross-section area A, containing a liquid to a height H, has an orifice at its base of area A/3 . The initial velocity of top surface of liquid is