Question

The Young's modulus of a metal is 2×10^12dyne/cm^2 and its breaking stress is 11000kg/cm^2. In case of longitudinal strain the maximum energy that can be stored per cubic metre of this metal is approximately (assume g=10m/s^2)
(1)58.25×10^5
(2)30.25×10^5
(3)37.15×10^5
(4)15.15×10^5

Answer 1

Use Youngs modulus = Stress/strain along with the formula,

Energy Stored per unit volume = (1/2)×stress×strain (with proper units)

Look up hcv for derivations!

Answer 2

Concept Introduction:-

It could take the shape of a word or a numerical representation of a quantity's arithmetic value.

Given Information:-

We have been given that The Young's modulus of a metal is $2\times 10^{12}$$dyne/cm^2$ and its breaking stress is $11000kg/cm^2$.

To Find:-

We have to find that the longitudinal strain the maximum energy that can be stored per cubic metre of this metal is approximately.

Solution:-

According to the problem

$Y=\frac{stress}{strain}\\\Rightarrow strain=\frac{stress}{Y}$

$Energy/m^3=energy density\\=\frac{1}{2} \times stress \times strain\\=\frac{1}{2} \times stress \times \frac{stress}{Y}\\=\frac{stress^2}{2Y}$

For maximum energy/$m^3$$=\frac{(Breaking Stress)^2}{Y}\\={\frac(11000\times 10)^2{10^{4}}}\times \frac{10^{-4}}{2 \times 2 \times 10^{12}\times 10^{-5}}}\\=30.25 \times 10^5$J

Final Answer:-

The correct answer is $(2)30.25\times 10^5$.

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