Question

The force required to double the length of a steel wire of area 1 cm², if it's Young's modulus Y = `2 xx 10^11/m^2` is:

Options

• 2 × 10¹¹ N

• 2 × 10⁷N

• 6 × 10⁷N

• 2 × 10⁹N

Answer 1

2 × 10¹¹ N

Explanation:

Given,

Steel wire Young's modulus, Y = 2 × 10¹¹ 

steel wire area A = 1 cm²

Let l be the starting length = l

Total length =  2l

Variation in length Δl = 2l = l

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

= `"F"/"A" xx "l"/(Δ"l")`

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

⇒ F = `2 xx 10^11"N"`