A cubical block of side $0.5\,m$ floats on water with $30\%$ of its volume under water. ....... $kg$ is the maximum weight that can be put on the block without fully submerging it under water ? [Take density of water $= 10^3\,kg/m^3$ ]
JEE MAIN 2019, Diffcult
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$0.3\,{\ell ^3}\,{\rho _\omega } = {\ell ^3}\rho $
$\rho = 300\frac{{kg}}{{{m^3}}}$
$m + {\ell ^3}\rho = {\ell ^3}{\rho _\omega }$
$M = {\ell ^3}\left( {{\rho _w} - \rho } \right) = {\left( 0.5 \right)^3}\left\{ {1000 - 300} \right\}$
$ = 700 \times {\left( 0.5 \right)^3}$
$ = 87.5\,kg$
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