a steel fire of internal diameter 80 cm 20°c is to be fitted on a wheel of diameter 80.5cm to what temperature must the tire be heated to just fill the wheel?(linear expansion of steel =12×10^-6per kelvin
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Answer:
The diameter of (d) of iron tyre should be equal to ⊥m i.e., 1000 mm
The initial diameter (d) of iron tyre
=1m−6mm
=(1000−6)mm
=994 mm
we have
cubical expressin (
r
ˉ
)=3.6×10
−5
/
o
C
⇒ 3α=3.6×10
−5
⇒ α=1.2×10
−5
/
o
C
where
α→linear expression
Now, we know that
l=l
0
(⊥+αΔθ)
there,
d=d
0
(⊥+αΔθ)
1000=994(⊥+1.2+10
−5
Δθ)
⇒994×1.2×10
−5
Δθ=6
⇒ Δθ=
994×1.2
6
×10
5
=503
o
C
⇒ Δθ≅500
o
C
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