Fluid mechanics

The figure above shows a cubical block of side \(10\text{ cm} \) and relative density 1.5 suspended by a wire of cross-sectional area \(10^{-6} \text{ m}^2\). The breaking stress of the wire is \(7\times 10^6 \text{ N/m}^2\). The block is placed in a beaker of base area \(200\text{ cm}^2\) and initially i.e. at \(t=0\), the top surface of the water and the block coincide. There is a pump at the bottom corner which ejects \(2\text{ cm}^3\) of water per second. Find the time at which the wire will break.

Take \(g = 10\text{ m/s}^2\).

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