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 102 cm- - of material of wire is

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Young's Modulus of Elasticity

A wire of len...

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 $100^{\circ}$ C, the length of the gap increases to 1)02 cm. $α$ of material of wire is

2 \times 10^{- 4} /^{\circ} C

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4 \times 10^{- 4} /^{\circ} C

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6 \times 10^{- 4} /^{\circ} C

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1 \times 10^{- 4} /^{\circ} C

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Solution

The correct option is C $2 \times 10^{- 4} /^{\circ} C$
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 cm become 1.02 cm, 60 cm will become 61.2 cm
So, change in length $= 61.2$ cm $- 60$ cm $=$ 1.2 cm
original length is 60 cm and change in temperature $=$ $100^{0}$ C
Putting these values in the formula of $α = \frac{d l}{l \times d t}$ , where $d l =$ Change in length and $d t =$ change in temperature, we get, $α = 2 \times 10^{- 4} /^{\circ}$ C

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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 wire of length 60 cm is bent into a circle with a gap of 1 cm. At its ends, on heating it by $100^{\circ}$ C, the length of the gap increases to 1)02 cm. $α$ of material of wire is