Question

a wooden wheel has a diameter of 100cm at 0°c ,an iron tyre whose diameter at 0°c is 99.5 is to be fitted on to the wooden wheel. if the co efficient of linear expansion of iron id 12x10-6 per °c then the temperature to which tyre must be heated to fit it on to the wooden tyre :
210°c
420°c
42°c
84.4°c​

Answer 1

Explanation:

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