Q96 / 160 · JIPMER 2010 · Physics
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
- A200N
- B400N
- C600N
- Correct answerD800N
Solution
Yaung's modulus
$Y=\frac{F L}{A l} \text { or } F=\frac{Y A l}{L}$
or $F \propto A$ or $F \propto r^2$ or $F \propto d^2$
$\therefore \quad \frac{F_1}{F_2}=\frac{d_1^2}{d_2^2}$
Given, $d_1=d, d_2=2 d, F_1=200 \mathrm{~N}$
$\begin{array}{ll}
\therefore & \frac{200}{F_2}=\frac{(d)^2}{(2 d)^2}=\frac{1}{4} \\
\text { or } & F_2=4 \times 200=800 \mathrm{~N}
\end{array}$
Hence, the correct answer is option: 'D'.