Spheres of iron and lead having the same mass | vedclass

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(A) According to Archimedes' principle,the apparent loss of weight of an object immersed in a fluid is equal to the weight of the fluid displaced by i

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(A) According to Archimedes' principle,the apparent loss of weight of an object immersed in a fluid is equal to the weight of the fluid displaced by it.Loss of weight $w = V \rho_{w} g$,where $V$ is the volume of the object and $\rho_{w}$ is the density of water.Since the mass $m$ of both spheres is the same,we have $m = V_{iron} \rho_{iron} = V_{lead} \rho_{lead}$.Thus,the volume $V = \frac{m}{\rho}$.Substituting this into the expression for loss of weight: $w = \frac{m}{\rho} \rho_{w} g = m g \frac{\rho_{w}}{\rho}$.For the iron sphere,$w_{1} = m g \frac{\rho_{w}}{\rho_{iron}}$.For the lead sphere,$w_{2} = m g \frac{\rho_{w}}{\rho_{lead}}$.Taking the ratio: $\frac{w_{1}}{w_{2}} = \frac{\rho_{lead}}{\rho_{iron}}$.Since the density of lead is greater than the density of iron $(\rho_{lead} > \rho_{iron})$,it follows that $\frac{w_{1}}{w_{2}} > 1$.

Spheres of iron and lead having the same mass are completely immersed in water. The density of lead is greater than that of iron. If the apparent loss of weight is $w_{1}$ for the iron sphere and $w_{2}$ for the lead sphere,then the ratio $\frac{w_{1}}{w_{2}}$ is:

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