A vertical metal cylinder of radius 2 cm and length 2 m is fixed at its lower end, and a load of 100 kg is placed on it. Determine the compression of the cylinder. The Young modulus of the metal is 2 × 10^ 11 N/m^2 .

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Quantrex Academy · Accepted Answer

Correct answer: A. 8 × 10^ -6 m

The compression of the cylinder is given by the formula for Young's modulus:

Y = \dfrac{F L}{A \Delta L} \Rightarrow \Delta L = \dfrac{F L}{A Y}

The force applied is the weight of the load. Taking

g = 10 \text{ m/s}^2

:

F = mg = 100 \times 10 = 1000 \text{ N}

The cross-sectional area of the cylinder is:

A = \pi r^2 = \pi \times (2 \times 10^{-2})^2 = 4\pi \times 10^{-4} \text{ m}^2

Substituting the given values into the formula:

\Delta L = \dfrac{1000 \times 2}{4\pi \times 10^{-4} \times 2 \times 10^{11}}

\Delta L = \dfrac{2000}{8\pi \times 10^7}

\Delta L = \dfrac{250}{\pi} \times 10^{-7} \text{ m}

Using

\pi \approx 3.14

:

\Delta L \approx 79.6 \times 10^{-7} \text{ m} \approx 8 \times 10^{-6} \text{ m}

A vertical metal cylinder of radius 2 cm and length 2 m is fixed at...

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