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KVPY SA Exam 2011 Question Paper
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© examsnet.com
Question : 66
Total: 80
PHYSICS
An object with uniform density ρ is attached to a spring that is known to stretch linearly with applied force as shown below.
When the spring-object system is immersed in a liquid of density
ρ
1
as shown in the figure, the spring stretches by an amount
x
1
(
ρ
>
ρ
1
)
. When the experiment is repeated in a liquid of density
ρ
2
<
ρ
1
, the spring stretches by an amount
x
2
. Neglecting any buoyant force on the spring, the density of the object is
ρ
=
ρ
1
x
1
−
ρ
2
x
2
x
1
−
x
2
ρ
=
ρ
1
x
2
−
ρ
2
x
1
x
2
−
x
1
ρ
=
ρ
1
x
2
+
ρ
2
x
1
x
2
+
x
1
ρ
=
ρ
1
x
1
+
ρ
2
x
2
x
1
+
x
2
Validate
Solution:
k
x
1
+
ρ
1
V
g
=
ρ
V
g
…(1)
k
x
2
+
ρ
2
V
g
=
ρ
V
g
…(2)
from (1) and (2)
ρ
=
ρ
2
x
1
−
ρ
1
x
2
x
1
−
x
2
=
ρ
1
x
2
−
ρ
2
x
1
x
2
−
x
1
© examsnet.com
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