Question

A rubber cord of length 40cm and area of cross section $4 \times 10^{-6} \, m^2$ is extended by 10cm. If the energy gained is 20 joule, (young's modulus of rubber is

• A. $10^8\,Nm^{-2}$
• B. $2 \times 10^8\,Nm^{-2}$
• C. $4 \times 10^8\,Nm^{-2}$
• D. $1.5 \times 10^8\,Nm^{-2}$

Answer 1

Answer: (C)

Energy $=\frac{ AY }{2 L } l ^{2}$
$20=\frac{4 \times 10^{-6} \times Y \times\left(\frac{10}{100}\right)^{2}}{2 \times \frac{40}{100}}$
$Y =\frac{20 \times 2 \times 40}{4 \times 10^{-6} \times\left(\frac{10}{100}\right)^{2} \times 100}$
$=4 \times 10^{8} N / m ^{2}$