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Q.

A cube of wood of mass 0.5 kg and density 800 kg m-3 is fastened to the free end of a vertical spring of spring constant k= 50Nm-1, fixed at the bottom. Now, the entire system is completely submerged in water. The elongation or compression of the spring in equilibrium is β2 cm. The value of β is __. (Given, g= 10 ms-2)

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answer is 5.

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Detailed Solution

ρs<ρw So, block tends to move up and thus the spring has elongation.BF=mg×kxVρwg=Vρsg+kx0.8800×1000×10=(0.5)(10)+50xx=0.025m=2.5cm=52cm⇒β=5
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