A wire can be broken by applying load of 200 N . The force required...

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

Options

A200N
B400N
C600N
D800N

Correct answer

D. 800N

Step-by-step solution

Yaung's modulus

Y=\frac{F L}{A l} \text{ or } F=\frac{Y A l}{L}

F \propto A

F \propto r^2

F \propto d^2 \therefore \quad \frac{F_1}{F_2}=\frac{d_1^2}{d_2^2}

Given,

d_1=d, d_2=2 d, F_1=200 \mathrm{ N}

\begin{array}{ll} \therefore & \frac{200}{F_2}=\frac{(d)^2}{(2 d)^2}=\frac{1}{4} \\ \text{ or } & F_2=4 \times 200=800 \mathrm{ N} \end{array}

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