Respuesta :
Answer with Explanation:
The crown will be pure if it's specific gravity is 19.3
Now by definition of specific gravity it is the ratio between the weight of an object to the weight of water of equal volume
Since it is given that the weight of the crown is 11.8 N we need to find it's volume
Now According to Archimedes principle when the crown is immersed into water the water shall exert a force in upwards direction on the crown with a magnitude equaling to weight of the water displaced by the crown
Mathematically this is the difference between the weight of the crown in air and weight when immersed in water
Thus Buoyant force is [tex]F_{B}=11.8-10.9=0.9N[/tex]
Now by Archimedes principle This force equals in magnitude to the weight of water of same volume as of the crown
Thus the specific gravity of the crown equals
[tex]S.G=\frac{11.8}{0.9}=13.11[/tex]
As we see that the specific gravity of the crown material is less than that of pure gold hence we conclude that it is impure.
The crown is not made of pure gold.
Given:
[tex]\to SG_{gold} = 19.3 \\\\[/tex]
weight of air [tex]W_{air} = 11.8\ N \\\\[/tex]
water weight [tex]W_{water} = 10.9 \ N \\\\[/tex]
To Find:
using the buoyancy B that calculates the difference of weight=?
Solution:
Using formula:
[tex]\to B = W_{air} - W_{water} \\\\[/tex]
[tex]= 11.8\ N - 10.9\ N\\\\ = 0.9 \ N\\\\[/tex]
Using a formula for calculating weight:
[tex]\to W_{air} = SG_{\gamma water}\times V_{crown}\\\\ \to W_{water} = B(SG - 1)[/tex]
calculating the [tex]\bold{SG_{crown}}[/tex]:
[tex]\to SG_{crown}=1+\frac{W_{water}}{B} \\\\[/tex]
[tex]= 1 + \frac{10.9\ N}{0.9\ N}\\\\= 1 + 12.11\\\\= 13.11[/tex]
Knowing that the [tex]SG_{gold}= 19.3[/tex] indicates that the crown is not made of pure gold.
[tex]\to \bold{SG_{crown}= 13.1}[/tex] The crown is not composed entirely of gold.
Find out more information about the gold here:
brainly.com/question/900003
