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)

If the cylinder is pushed down from equilibrium by a distance which is half the distance as calculated in the above question, determine time period of subsequent motion.

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

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

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) By what maximum distance cylinder will be pushed downward into the liquid from equilibrium position so that when it is set free then tension in the string will not vanish [Assume at equilibrium position system was at rest]

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) By what maximum distance cylinder will be pushed downward into the liquid from equilibrium position so that when it is set free then tension in the string will not vanish [Assume at equilibrium position system was at rest]

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

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 the length of the block. if acceleration due to gravity is g, the spring constant of the spring is

A block of mass m is connected to another .block of mass M by a massless spring of spring constant k. A constant force f starts action as shown in figure, then:

A block of mass m is connected to another .block of mass M by a massless spring of spring constant k. A constant force f starts action as shown in figure, then:

A solid cylinder of length l and cross-sectional area A is made of a material whose resistivity depends on the distance r from the axis of the cylinder as rho = k//r^(2) where k is constant . The resistance of the cylinder is -

Two springs are connected to a block of mass M is placed on a frictionless surface as shown in figure. If both springs have a spring constant k, the frequency of oscillation of the block is………