Question

A uniform cylinder 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 liquid of density σ at equilibrium position. The extension of the spring when it is in equilibrium is:

• A. $\frac{Mg}{K}$
• B. $\frac{Mg}{K}(1-\frac{LA\sigma }{M})$
• C. $\frac{Mg}{K}(1-\frac{LA\sigma }{2M})$
• D. $\frac{Mg}{K}(1+\frac{LA\sigma }{2M})$

Answer 1

The correct option is C $\frac{Mg}{K}(1-\frac{LA\sigma }{2M})$

At equilibrium,
$K{x}_0+F_B=Mg$

or $K{x}_0+\frac{AL}{2}\sigma g=Mg$

$x_0=\frac{Mg-\frac{LA\sigma g}{2}}{k}$

= $\frac{mg}{K}(1-\frac{LA\sigma }{2M})$