A wire can be broken by applying load of 200 N. The force required to break another wire of the same length and same material, but double in diameter is

200 N

400 N

600 N

800 N

Solution

600 N

Young's modulus

Y = $\frac{F L}{A l}$

F = $\frac{Y A l}{L}$

F ∝ A

⇒ F ∝ r²

⇒ F ∝ d²

∴ $\frac{F_{1}}{F_{2}} = \frac{d_{1}^{2}}{d_{2}^{2}}$

Given:- d₁ = d, d₂ = 2d and F₁ = 200N

∴ $\frac{200}{F_{2}} = \frac{{(d)}^{2}}{{(2 d)}^{2}}$

= $\frac{1}{4}$

⇒ F₂ = 4 × 200

F₂ = 800 N

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