First slide

Pressure in a fluid-mechanical properties of fluids

Question

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 $\frac{β}{2}$ cm. The value of $β$ is __. (Given, g= 10 ms^-2)

Moderate

Solution

$ρ_{s} < ρ_{w}$ So, block tends to move up and thus the spring has elongation.
$\begin{array}{l} B_{F} = m g \times k x \\ V ρ_{w} g = V ρ_{s} g + k x \\ \frac{0.8}{800} \times 1000 \times 10 = (0.5) (10) + 50 x \\ x = 0.025 m = 2.5 cm = \frac{5}{2} cm \\ \Rightarrow β = 5 \end{array}$

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