Question

Two wires having same length and material are stretched by same force. Their diameters are in the ratio 1: 3. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched is ______.

Options

• 3 : 1

• 9 : 1

• 27 : 1

• 81 : 1

Answer 1

Two wires having same length and material are stretched by same force. Their diameters are in the ratio 1: 3. The ratio of strain energy per unit volume for these two wires (smaller to larger diameter) when stretched is 9 : 1.

Explanation:

Energy per unit volume in string is given by

`1/2` × stress × strain

i.e. `"U"/"V"=1/2xx"F"/"A"xx(Delta"l")/"l"` 

= `1/2` × Y × (strain)²

∴ `"U"_"s"/"S"_"L"="Y"_"s"/"Y"_"L"xx(("Stress"("S"))/("strain"("L")))^2`

= `"A"_"L"/"A"_"s"=("l"/"l")^2`

⇒ `"r"_"L"^2/"r"_"s"^2=3^2/1^2`

= 9 : 1