Gold artefacts unearthed from an archaeological site included a gold status
weighing 21 kg 50 g, 2 necklaces weighing 3.520 kg each, and 3 pairs of
earrings weighing 85 g.
(a) How heavy is the statue compared to the two necklaces?
(b) What is the total weight of the unearthed gold items?
Answers
Answer:
Given :
Weight of ornament in air, W
air
=36g
Weight of ornament in water, W
water
=34g
Specific gravity of gold, ρ
g
=19.3g/cc
Specific gravity of copper, ρ
c
=8.9g/cc
Let V
c
be the volume of copper and V
g
be the volume 0 gols
Loss of weight = weight of displacement water (buoyance) =36−34=2g
W=V
g
×ρ
g
×g+V
c
×ρ
c
×g
36g=19.3V
g
×g+8.9V
c
×g
⇒m
g
+m
c
=36⟶(1)
Now, (V
g
+V
c
)ρ
w
×g=2×g
⇒(
ρ
g
m
g
+
ρ
c
m
c
)ρ
w
×g=2×g
⇒(
19.3
m
g
+
8.9
m
c
)=2⟶(2)
Solving (1) and (2)
mass of gold in orrnament, m
g
=33.75
mass of copper in ornament, m
c
=2.225
Since, the goldsmith argues that he has not mixed copper or any other material with gold, rather some cavities might have been left inside the ornament.
Now, ⇒(
ρ
g
m
g
+V
cavity
)ρ
w
×g=2×g
⇒(
19.3
33.75
+V
cavity
)=2⇒V
cavity
=0.251
Step-by-step explanation:
Given :
Weight of ornament in air, W
air
=36g
Weight of ornament in water, W
water
=34g
Specific gravity of gold, ρ
g
=19.3g/cc
Specific gravity of copper, ρ
c
=8.9g/cc
Let V
c
be the volume of copper and V
g
be the volume 0 gols
Loss of weight = weight of displacement water (buoyance) =36−34=2g
W=V
g
×ρ
g
×g+V
c
×ρ
c
×g
36g=19.3V
g
×g+8.9V
c
×g
⇒m
g
+m
c
=36⟶(1)
Now, (V
g
+V
c
)ρ
w
×g=2×g
⇒(
ρ
g
m
g
+
ρ
c
m
c
)ρ
w
×g=2×g
⇒(
19.3
m
g
+
8.9
m
c
)=2⟶(2)
Solving (1) and (2)
mass of gold in orrnament, m
g
=33.75
mass of copper in ornament, m
c
=2.225
Since, the goldsmith argues that he has not mixed copper or any other material with gold, rather some cavities might have been left inside the ornament.
Now, ⇒(
ρ
g
m
g
+V
cavity
)ρ
w
×g=2×g
⇒(
19.3
33.75
+V
cavity
)=2⇒V
cavity
=0.251