A uniform cylindrical block of length `l` density `d_(1)` and area of cross section A floats in a liquid of density `d_(2)` contained in a vessel `(d_(2) gt d_(1))`. The bottom of the cylinder just rests on a spring of contant k. The other end of the spring is fixed to the bottom of the vessel. A weight that may be placed on top of the cylinder such that the cylinder is just submerged in the liquid. find the weight.

An object weights m_(1) in a liquid of density d_(1) and that in liquid of density d_(2) is m_(2) . The density of the object is

A body of density d_(2) is dropped from rest at a height x into a beaker having a liquid of density d_(1)(d_(2)gtd_(1)) . Which of the following is/are true?

A cubical block of wood of edge a and density rho floats in water of density 2rho . The lower surface of the cube just touches the free end of a mass less spring of force constant K fixed at the bottom of the vessel. The weight W put over the block so that it is completely immersed in water without wetting the weight is

Consider a solid cylinder of the density rho_(s) cross section area A and h ploating in a liquid of density rho_(l) as shown in figure (rho_(l) gt rho_(s)) . It is depressed sligtly and allowed to oscillation.

A cylinder of mass M and density d_(1) hanging from a string, is lowered into a vessel of cross-sectional area A, containing a liquid of density d_(2) (d_(2) lt d_(1)) until it is fully immersed. The increase in pressure at the bottom of the vessel is

A vertical pole of length l , density rho , area of cross section A , floats in two immiscible liquids of densities rho_(1) and rho_(2) . In equilibrium position the bottom end is at the interface of the liquids. When the cylinder is displaced vertically, the time period of oscillation is..........

A vertical pole of length l , density rho , area of cross section A floats in two immiscible liquids of densities rho_(1) and rho_(2) . In equuilibrium possition the bottom end is at the interface of the liquids. When the cylinder is displaced vertically, find the time period of oscillation.

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

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