SATHEE: Properties Of Solids And Liquids Question 265

Properties Of Solids And Liquids Question 265

Question: A concrete sphere of radius R has a cavity of radius r which is packed with sawdust. The specific gravities of concrete and sawdust are respectively 2.4 and 0.3 for this sphere to float with its entire volume submerged under water. Ratio of mass of concrete to mass of sawdust will be [AIIMS 1995]

Options:

A)8

B)4

C)3

D)Zero

Show Answer

Answer:

Correct Answer: B

Solution:

Let specific gravities of concrete and saw dust are $ρ_{1}$ and $ρ_{2}$ respectively.

According to principle of floatation weight of whole sphere = upthrust on the sphere $\frac{4}{3} π (R^{3} - r^{3}) ρ_{1} g + \frac{4}{3} π r^{3} ρ_{2} g = \frac{4}{3} π R^{3} \times 1 \times g$

therefore $R^{3} ρ_{1} - r^{3} ρ_{1} + r^{3} ρ_{2} = R^{3}$

therefore $R^{3} (ρ_{1} - 1) = r^{3} (ρ_{1} - ρ_{2})$

therefore $\frac{R^{3}}{r^{3}} = \frac{ρ_{1} - ρ_{2}}{ρ_{1} - 1}$

therefore $\frac{R^{3} - r^{3}}{r^{3}} = \frac{ρ_{1} - ρ_{2} - ρ_{1} + 1}{ρ_{1} - 1}$

therefore $\frac{(R^{3} - r^{3}) ρ_{1}}{r^{3} ρ_{2}} = (\frac{1 - ρ_{2}}{ρ_{1} - 1}) \frac{ρ_{1}}{ρ_{2}}$

therefore $\frac{Mass of concrete}{Mass of saw dust} = (\frac{1 - 0.3}{2.4 - 1}) \times \frac{2.4}{0.3} = 4$

Properties Of Solids And Liquids Question 265

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Properties Of Solids And Liquids Question 265

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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