A lady purchases a cheap "gold" crown at a flea (street) market. After she gets home, she hangs the crown from a scale and finds its weight to be 7.84 N [see fig.22(a)]. She then weighs the crown while it is immersed in water, and the scale reads 6.86 N [see fig.22(b)]. Is the crown made of pure gold ? Explain.
Take, Density of gold =19,300 kg/m3; dens g=9.8 m/s2. Solution Given, weight of crown in air, W1=7.84 N;
density of water, ρL=1000 kg/m3;
weight of crown in water, W2=6.86 N;
density of crown, ρs= ?
Now, weight of gold crown in air, W1 or ρs,Vsg=7.84− (1) where, V is the volume of the crown.
Buoyant force, FB= loss of weight in a liquid
or FB=W1−W2=7.84−6.86=0.98 N
Also, FB= weight of liquid displaced =mLg=ρLVLg=ρLVgg
(Vs=VL, because crown is completely immersed in water)
or ρLVsg=0.98− (2)
(2)(1)⇒ρLVsgρiVsg=0.987.84 or ρLρs=0.987.84=8
or ρs=8×ρL=8×1000=8000 kg/m3
Since, the density of gold is 19,300 kg/m3, the crown is certainly not pure.
It is either hollow, made of an alloy, or both.
CHECK YOUR CONCEPTS 3

Question

A lady purchases a cheap "gold" crown at a flea (street) market. After she gets home, she hangs the crown from a scale and finds its weight to be 7.84 N [see fig.22(a)]. She then weighs the crown while it is immersed in water, and the scale reads 6.86 N [see fig.22(b)]. Is the crown made of pure gold ? Explain.
Take, Density of gold =19,300 kg/m3; dens g=9.8 m/s2. Solution Given, weight of crown in air, W1​=7.84 N;
density of water, ρL​=1000 kg/m3;
weight of crown in water, W2​=6.86 N;
density of crown, ρs​= ?
Now, weight of gold crown in air, W1​ or ρs​,Vs​g=7.84− (1) where, V is the volume of the crown.
Buoyant force, FB​= loss of weight in a liquid
or FB​=W1​−W2​=7.84−6.86=0.98 N
Also, FB​= weight of liquid displaced =mL​g=ρL​VL​g=ρL​Vg​g
(Vs​=VL​, because crown is completely immersed in water)
or ρL​Vs​g=0.98− (2)
(2)(1)​⇒ρL​Vs​gρi​Vs​g​=0.987.84​ or ρL​ρs​​=0.987.84​=8
or ρs​=8×ρL​=8×1000=8000 kg/m3
Since, the density of gold is 19,300 kg/m3, the crown is certainly not pure.
It is either hollow, made of an alloy, or both.
CHECK YOUR CONCEPTS 3

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Question Text	A lady purchases a cheap "gold" crown at a flea (street) market. After she gets home, she hangs the crown from a scale and finds its weight to be $7.84 N$ [see fig.22(a)]. She then weighs the crown while it is immersed in water, and the scale reads $6.86 N$ [see fig.22(b)]. Is the crown made of pure gold ? Explain. Take, Density of gold $= 19, 300 kg / m^{3}$ ; dens $g = 9.8 m / s^{2}$ . Solution Given, weight of crown in air, $W_{1} = 7.84 N$ ; density of water, $ρ_{L} = 1000 kg / m^{3}$ ; weight of crown in water, $W_{2} = 6.86 N$ ; density of crown, $ρ_{s} =$ ? Now, weight of gold crown in air, $W_{1}$ or $ρ_{s}, V_{s} g = 7.84 -$ (1) where, $V$ is the volume of the crown. Buoyant force, $F_{B} =$ loss of weight in a liquid or $F_{B} = W_{1} - W_{2} = 7.84 - 6.86 = 0.98 N$ Also, $F_{B} =$ weight of liquid displaced $= m_{L} g = ρ_{L} V_{L} g = ρ_{L} V_{g} g$ $(V_{s} = V_{L}$ , because crown is completely immersed in water) or $ρ_{L} V_{s} g = 0.98 -$ (2) $\frac{( 1 )}{( 2 )} \Rightarrow \frac{ρ _{i} V _{s} g}{ρ _{L} V _{s} g} = \frac{7.84}{0.98}$ or $\frac{ρ _{s}}{ρ _{L}} = \frac{7.84}{0.98} = 8$ or $ρ_{s} = 8 \times ρ_{L} = 8 \times 1000 = 8000 kg / m^{3}$ Since, the density of gold is $19, 300 kg / m^{3}$ , the crown is certainly not pure. It is either hollow, made of an alloy, or both. CHECK YOUR CONCEPTS 3
Updated On	Nov 8, 2022
Topic	Physics
Subject	Science
Class	Class 9
Answer Type	Video solution: 1
Upvotes	58
Avg. Video Duration	8 min

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