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  4. A cubical block of side 0.5 m floats on water with 30 % of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water? [Take, density of water =103 k g / m3 ]

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Q. A cubical block of side $0.5 \, m$ floats on water with $30\%$ of its volume under water. What is the maximum weight that can be put on the block without fully submerging it under water?
[Take, density of water $ \, =10^{3} \, k g / m^{3}$ ]

NTA AbhyasNTA Abhyas 2022

Solution:

In first case, when $30\%$ of the cube inside water,
$\rho _{w}V_{i n} \, g=\rho _{c}Vg$
$\frac{V_{i n}}{V}=\frac{\rho _{c}}{\rho _{w}}=0.3$
Additional weight we can put $w$ is,
$V\rho _{w}g=\rho _{c}Vg+w$
$w = V \left(\rho_{ W }-\rho_{ c }\right) g$
$=\left(0.5\right)^{3}\times 0.7\times \left(10\right)^{3}\times g$
$=87.5g \, N$
Addition of mass that we can put $=87.5 \, kg$