A uniformcylinder of length L and mass M having cross - sectional area A is suspended , with its length vertical from a fixed point by a massless spring , such that it is half submerged in a liquidof density sigma atequilibrium position .The extension x_(0)of the spring when it is in equilibrium is .

A uniformcylinder of length L and mass M having cross - sectional area

1.	A uniformcylinder of length L and mass M having cross - sectional area A is suspended , with its length vertical from a fixed point by a massless spring , such that it is half submerged in a liquidof density sigma atequilibrium position .The extension x_(0)of the spring when it is in equilibrium is .
Answer» `(MG)/k ` `(Mg)/k (1-(LAsigma)/M)` `(Mg)/k (1-(LAsigma)/(2M))` `(Mg)/k (1+(LAsigma)/M)` Solution : Mass of cross section A , `M = (AL)/2 ` and LENGTH `L/2 ` ` :. ` Buoyant force in liquid of sensity `sigma ` `F_(B) = igma Mg = sigma (Alg)/2 ` Suppose extension of spring is `x_(0)` ` :. ` Restoring force in upward direction in spring ` = kx_(0)` When k = spring constant and force of WEIGHT on the cylinder in downward direction = Mg ` :. ` For equilibrium condition of cylinder , ` :. mg = (sigmaALg)/2 + kx_(0)` ` :. kx_(o)=mg - (sigmaALg)/2 ` ` :. x_(0) =(mg-(sigmaALg)/2)/k` ` :. x_(0) =(Mg)/k (1- (sigmaLA)/(2M))`