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  • A cubical block of steel of each side equal to is floating on mercury in a vessel. The densities of s

A cubical block of steel of each side equal to \mathrm{l} is floating on mercury in a vessel. The densities of steel and mercury are \mathrm{\rho_s} and \mathrm{\rho_m}. The height of the block above the mercury level is given by

Option: 1

\mathrm{l\left(1+\frac{\rho_s}{\rho_m}\right)}


Option: 2

\mathrm{l\left(1-\frac{\rho_s}{\rho_m}\right)}


Option: 3

\mathrm{l\left(1+\frac{\rho_m}{\rho_s}\right)}


Option: 4

\mathrm{l\left(1-\frac{\rho_m}{\rho_s}\right)}


Answers (1)

best_answer

Volume of block \mathrm{=l^3. } Let h be the height of the block above the surface of mercury. Volume of mercury displaced \mathrm{=(l-h) l^2.}

\therefore \quad  Weight of mercury displaced \mathrm{=(l-h) l^2 \rho_m g.}

This is equal to the weight of the block which is \mathrm{\rho_s l^3 g.}

Thus \mathrm{\quad(l-h) l^2 \rho_m g=\rho_s l^3 g}

which gives \mathrm{ h=l\left(1+\frac{\rho_s}{\rho_m}\right) }

Posted by

vinayak

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