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Manipal Entrance Test 2015 Physics Paper
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© examsnet.com
Question : 49
Total: 50
When a copper sphere is heated, percentage change is
maximum in radius
maximum in volume
maximum in density
equal in radius, volume and density
Validate
Solution:
Let
R
be the radius of sphere,
V
its volume and
ρ
its density. Then,
Δ
R
=
R
α
Δ
θ
and percentage change in radius
Δ
R
R
×
100
=
100
α
Δ
θ
...(i)
Now,
Δ
V
=
γ
v
Δ
θ
=
3
α
v
Δ
θ
(
∵
γ
=
3
α
)
∴ Percentage increase in volume
=
Δ
V
V
×
100
=
300
α
Δ
θ
...(ii)
Again,
ρ
′
=
ρ
1
+
γ
Δ
θ
=
ρ
1
+
3
α
Δ
θ
∴
Δ
ρ
=
ρ
−
ρ
′
=
ρ
[
1
−
1
1
+
3
α
Δ
θ
]
=
(
3
α
Δ
θ
)
ρ
1
+
3
α
Δ
θ
Percentage change in density
=
Δ
ρ
ρ
×
100
=
300
α
Δ
θ
1
+
3
α
Δ
θ
...(iii)
From Eqs. (i), (ii) and (iii), we see that the percentage change is maximum in volume.
© examsnet.com
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