ISRO Mechanical & Aerospace 2011 - Question 7

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A cylindrical body of cross-sectional area A, height H and density $\rho_s$, is immersed to a depth h in a liquid of density $\rho$, and tied to the bottom with a string. The tension in the string is

Figure for question 7, ISRO Mechanical & Aerospace 2011

  • A. $\rho ghA$
  • B. $(\rho h - \rho_s H)gA$
  • C. $(\rho - \rho_s)ghA$
  • D. $(\rho_s - \rho)ghA$

Answer: B. $(\rho h - \rho_s H)gA$

Explanation: Forces: Tension T (down) + Weight W (down) = Buoyancy B (up). $T = B - W = (\rho g A h) - (\rho_s g A H) = gA(\rho h - \rho_s H)$.

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