A wire of length 60 cm. Is bent into a circle with a gap of 1 cm. At its ends. On heating it by 100° C, the length of the gap increases to 1 .02 cm, α of material of wire is

Question

A wire of length 60 cm. Is bent into a circle with a gap of 1 cm. At its ends. On heating it by 100° C, the length of the gap increases to 1 .02 cm, α of material of wire is (A) 2× 10-4 /° C (B) 4× 10-4 /° C (C) 6× 10-4 /° C (D) 1× 10-4 /° C

Tardigrade Admin · Accepted Answer

Since on heating the length of the wire increases, it expands outwards, making the size of the ring bigger. consequently, the gap in the ring also becomes bigger in the same proportion.
So, if

1 c m

become

1.02 c m, 60 c m

will become

61.2 c m

So, change in length

= 61.2 c m - 60 c m = 1.2 c m

original length is

60 c m

and change in temperature

= 10 0^{\circ} C

Putting these values in the formula of

α = \frac{d l}{l x d t}

, where

d l =

Change in length and

d t =

change in temperature, we get,

α = 2 \times 1 0^{- 4} /^{\circ} C

Q. A wire of length 60 cm. Is bent into a circle with a gap of 1 cm. At its ends. On heating it by $10 0^{\circ} C$ , the length of the gap increases to 1 .02 cm, $α$ of material of wire is

$2 \times 1 0^{- 4} /^{\circ} C$

$4 \times 1 0^{- 4} /^{\circ} C$

$6 \times 1 0^{- 4} /^{\circ} C$

$1 \times 1 0^{- 4} /^{\circ} C$

Q. A wire of length 60 cm. Is bent into a circle with a gap of 1 cm. At its ends. On heating it by 100∘C, the length of the gap increases to 1 .02 cm, α of material of wire is

2×10−4/∘C

4×10−4/∘C

6×10−4/∘C

1×10−4/∘C

Q. A wire of length 60 cm. Is bent into a circle with a gap of 1 cm. At its ends. On heating it by $10 0^{\circ} C$ , the length of the gap increases to 1 .02 cm, $α$ of material of wire is

$2 \times 1 0^{- 4} /^{\circ} C$

$4 \times 1 0^{- 4} /^{\circ} C$

$6 \times 1 0^{- 4} /^{\circ} C$

$1 \times 1 0^{- 4} /^{\circ} C$