Fluid mechanics

Classical Mechanics Level 2

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 $g = 10\text{ m/s}^2$ .

120 seconds 40 seconds 80 seconds 100 seconds

2 solutions

Kalyan M
May 19, 2017

It should be 200 sec ri8 because 2 cm of water level comes down so that multiplying it wi4th base area if vessel gives volume lost by pump this gives answer 200

Varun Lahoti
Sep 22, 2018

I got the ans as 200 sec

T+DVg=mg...... (1) Consider that only x cm of block is immersed in water. (i.e 10-x cm out of water) Then , T+Density of water (a^2 x)*g=mass of the block *g...(2)

Now, stress = T/Area of string Thus, T=7N.....(3) Now density of obj(D) =d(rel)*d(water)

D=(1.5) *1000 kg/m^3......(4)

Mass of obj =1.5kg

Substituting the values in(2) , 7+100x=15 x=0.08m=8cm

Volume ref.

(Area of base - Area of cube) (10-x)

=(200-100)(10-8) =200 cubic cm

Time at which the wire breaks =200/2=100 seconds.

Aadhya Desai - 2 years, 1 month ago

Fluid mechanics

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