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Class 11
>>Physics
>>Thermal Properties of Matter
>>Thermal Expansion
>>Two rods of the same length, have radii
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Two rods of the same length, have radii in the ratio 3:4. Their densities are respectively 8000 and 9000kg/m
3
. Their specific heats are in the ratio of 2:3.When the same amount of heat is supplied to both,the changes in their lengths are in the ratio. (If their linear coefficients are in the ratio 5:6)
Medium
Solution
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Correct option is B)
Heat supplied: Q=msΔθ where m is the mass of the rod, , s is the specific heat of the rod and Δθ is the temp difference.
Δl=lαΔθ where α is the co-efficient of linear expansion and l is the length before being heated.
m=πr
2
lρ
Combining the above relations
Q=πr
2
lρsΔθ
Q
1
=Q
2
given
∴πr
1
2
l
1
ρ
1
s
1
Δθ
1
=∴πr
2
2
l
2
ρ
2
s
2
Δθ
2
∴πr
1
2
l
1
ρ
1
s
1
(
l
1
α
1
Δl
1
)=πr
2
2
l
2
ρ
2
s
2
(
l
1
α
2
Δl
2
)
Given l
1
=l
2
∴
Δl
2
Δl
1
=
r
1
2
ρ
1
s
1
r
2
2
ρ
2
s
2
α
2
α
1
=(
3
4
)
2
8000
9000
2
3
6
5
=
2
5
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