-->

Mechanical Properties Of Fluids

Question
CBSEENPH11020284

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 the equilibrium position. The extension x0 of the spring when it is in equilibrium is

  • Mg over straight k
  • Mg over straight k open parentheses 1 minus LAσ over straight M close parentheses
  • Mg over straight k open parentheses 1 minus fraction numerator LAσ over denominator 2 straight M end fraction close parentheses
  • Mg over straight k open parentheses 1 plus LAσ over straight M close parentheses

Solution

C.

Mg over straight k open parentheses 1 minus fraction numerator LAσ over denominator 2 straight M end fraction close parentheses

At equilibrium ΣF = 0

kx subscript straight o space plus space open parentheses AL over 2 σg close parentheses minus Mg space equals 0
straight x subscript straight o space equals space Mg open square brackets 1 minus fraction numerator LAσ over denominator 2 straight M end fraction close square brackets