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Chapter 7: Problem 1034

A piece of solid weighs \(120 \mathrm{~g}\) in air, \(80 \mathrm{~g}\) in water and \(60 \mathrm{~g}\) in liquid the relative density of the solid and that of the solid and that of the liquid are respectively. (A) 3,2 (B) \(2,(3 / 4)\) (C) \((3 / 4), 2\) (D) \(3,(3 / 2)\)

Short Answer

Expert verified
The relative density of the solid is 3, and the relative density of the liquid is 2. The answer is (A) 3, 2.

Step by step solution

01

Understanding Archimedes' principle

Based on Archimedes' principle, when an object is submerged in a fluid, it experiences a buoyant force equal to the weight of the fluid it displaces. This force acts opposite to the force of gravity and reduces the apparent weight of the object when submerged in the fluid. The buoyant force can be calculated using the formula: \(Buoyant \ force = weight_{object \ in \ fluid} - weight_{object \ in \ air}\).
02

Calculate the buoyant force in water

We will calculate the buoyant force experienced by the solid in water using the given weights: Buoyant force in water = apparent weight of the solid in water - weight of the solid in air Buoyant force in water = \(80 \mathrm{~g} - 120 \mathrm{~g} = -40 \mathrm{~g}\)
03

Calculate relative density of solid

Relative density or specific gravity is the ratio of the density of a substance to that of a reference substance (water in this case). Using the calculated buoyant force in water, we can find the relative density of the solid: Relative density of solid = \(\frac{Weight \ of \ solid \ in \ air}{Weight \ of \ solid \ in \ air - Weight \ of \ solid \ in \ water}\) Relative density of solid = \(\frac{120 \mathrm{~g}}{40 \mathrm{~g}} = 3\)
04

Calculate the buoyant force in liquid

Now we will calculate the buoyant force experienced by the solid in the liquid using the given weights: Buoyant force in liquid = apparent weight of the solid in liquid - weight of the solid in air Buoyant force in liquid = \(60 \mathrm{~g} - 120 \mathrm{~g} = -60 \mathrm{~g}\)
05

Calculate relative density of liquid

We can find the relative density of the liquid in the same way as we found for the solid: Relative density of liquid = \(\frac{Weight \ of \ solid \ in \ air}{Weight \ of \ solid \ in \ air - Weight \ of \ solid \ in \ liquid}\) Relative density of liquid = \(\frac{120 \mathrm{~g}}{60 \mathrm{~g}} = 2\) So the answer is (A) relative density of the solid = 3, and relative density of the liquid = 2.

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