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A thin rod having a length of  \mathrm{1 m} and area of cross-section \mathrm{3 \times 10^{-6} m^{2}} is suspended vertically from one end. The rod is cooled from \mathrm{210^{0}C \: to\: 160^{0}C}. After cooling, a mass \mathrm{M} is attached at the lower end of the rod such that the length of rod again becomes 1 m. Young's modulus and coefficient of linear expansion of the rod are \mathrm{2 \times 10^{11} N m^{-2} \: and\: 2 \times 10^{-5} K^{-1}}, respectively. The value of \mathrm{M} is _____ \mathrm{kg.}
(Take \mathrm{g = 10 m s^{-2}})

Option: 1

60


Option: 2

-


Option: 3

-


Option: 4

-


Answers (1)

best_answer

\begin{aligned} & \mathrm{Y}=\frac{F L}{A \Delta L} \\ & \mathrm{F}=Y A\left(\frac{\Delta L}{L}\right) \\ & \mathrm{F}=Y A(\alpha \Delta T) \\ & \mathrm{Mg}=Y A(\alpha \Delta T) \\ & \mathrm{M} \times 10=2 \times 10^{11} \times 3 \times 10^{-6} \times 2 \times 10^{-5} \times 50 \\ & \mathrm{M}=60 \mathrm{~kg} \end{aligned}

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