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  • A wooden block of mass m and density is tied to a string; the other end of the string is

A wooden block of mass m and density \mathrm{\rho} is tied to a string; the other end of the string is fixed to the bottom of a tank. The tank is filled with a liquid of density \mathrm{\sigma } with \mathrm{\sigma>\rho}. What is the tension in the string.

Option: 1

\mathrm{\left(\frac{\sigma-\rho}{\sigma}\right) m g}


Option: 2

\mathrm{\left(\frac{\sigma-\rho}{\rho}\right) m g}


Option: 3

\mathrm{\frac{\rho m g}{\sigma}}


Option: 4

\mathrm{\frac{\sigma m g}{\rho}}


Answers (1)

best_answer

Volume of the block \mathrm{ =\frac{m}{\rho}}. Now upthrust = weight of water displaced = weight of volume \mathrm{m / \rho} of liquid \mathrm{=} mass of volume \mathrm{m / \rho} of liquid \mathrm{\times g=\frac{m \sigma g}{\rho}}. This is the upward force on the block due to buoyancy. The downward force on the block \mathrm{= } its weight \mathrm{=m g.}

The tension in the string is the net upward force on the block which is

\mathrm{ T=\frac{m \sigma g}{\rho}-m g=\left(\frac{(\sigma-\rho)}{\rho}\right) m g }

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Gunjita

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