Question

The force required to double the length of a steel wire of area 1 cm², if its Young's modulus Y= 2 × 10¹¹/m² is: 

Options

• 2 × 10¹¹ N

• 2 × 10⁷ N 

• 6 × 10⁷ N 

• 2 × 10⁹ N  

Answer 1

2 × 10¹¹ N

Explanation - 

Given,

Young's modulus of steel wire, Y= 2 × 10¹¹

Area of steel wire, A= 1 cm²

Let initial length = l

Final length = 2l

Change in length Δl = 2l - l = l

Young's modulus, `"Y" = ("F"/"A")/(triangle"l"/"l") = "F"/"A" xx "l"/(triangle"l")`

⇒ `2 xx 10^11 = "F"/"A" xx "l"/(triangle"l")`

⇒ `"F" = 2 xx 10^11` N