Spheres of iron and lead having the same mass | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Vedclass · Accepted Answer

$>1$

Vedclass · Answer

(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:

Similar Questions

$A$ hollow sphere of volume $V$ is floating on the water surface with half immersed in it. What should be the minimum volume of water poured inside the sphere so that the sphere now sinks into the water?

An air bubble of radius $1\,cm$ in water has an upward acceleration of $9.8\,cm\,s^{-2}$. The density of water is $1\,g\,cm^{-3}$ and water offers negligible drag force on the bubble. The mass of the bubble is $.......g$.
$(g = 980\,cm\,s^{-2})$

$A$ body when fully immersed in a liquid of specific gravity $1.2$ weighs $44 \text{ gwt}$. The same body when fully immersed in water weighs $50 \text{ gwt}$. The mass of the body is (in $\text{ g}$)

$A$ wooden cube of side $10 \ cm$ floats at the interface between water and oil with its lower surface $3 \ cm$ below the interface. If the density of oil is $0.9 \ g \ cm^{-3}$,the mass of the wooden cube is (in $g$)

$A$ body floats in water with $40 \%$ of its volume outside water. When the same body floats in oil, $60 \%$ of its volume remains outside oil. The relative density of the oil is

Vedclass Test Series

Exam Paper Generator

Online Exam Module