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Passage XIV) A uniform cylindrical block...

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]

A

`(3Mg)/(K+Arhog)`

B

`(3Mg)/(2(K+Arhog))`

C

`(8Mg)/(3(K+Arhog))`

D

`(3Mg)/(2K + 3Arhog)`

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The correct Answer is:
A
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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) 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.

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