(D) Given: Diameter $d = 0.015 \ m$, Length $L = 0.2 \ m$. The relation is $F = 97.2 \times 10^6 (\Delta L)$. The formula for Young's modulus is $Y =

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(D) Given: Diameter $d = 0.015 \ m$, Length $L = 0.2 \ m$. The relation is $F = 97.2 \times 10^6 (\Delta L)$. The formula for Young's modulus is $Y = \frac{F L}{A \Delta L}$. The area of cross-section $A = \pi r^2 = \pi (d/2)^2 = \frac{\pi d^2}{4}$. Substituting $A$: $Y = \frac{F L}{(\pi d^2 / 4) \Delta L} = \frac{4 F L}{\pi d^2 \Delta L}$. From the given relation, $\frac{F}{\Delta L} = 97.2 \times 10^6 \ N/m$. Substituting the values: $Y = \frac{4 \times (97.2 \times 10^6) \times 0.2}{3.14159 \times (0.015)^2}$. $Y = \frac{77.76 \times 10^6}{0.00070685} \approx 110 \times 10^9 \ Pa = 110 \ GPa$.

Class 11 Physics Mechanical Properties of Solids Young’s Modulus

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In a tensile test on a metal bar of diameter $0.015 \ m$ and length $0.2 \ m$, the relation between the load and elongation within the proportional limit is found to be $F = 97.2 \times 10^6 (\Delta L)$, where $F$ is the load in $N$ and $\Delta L$ is the elongation in $m$. The Young's modulus of the material in $GPa$ is:

TS EAMCET 2018 All TS EAMCET

A
$75.5$
B
$85.6$
C
$98.7$
D
$110$

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Mechanical Properties of Solids

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Young’s Modulus

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Write the equation of bending in a rod. Write the unit of bending and its dimensional formula.

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$A$ structural steel rod has a radius of $10 \;mm$ and a length of $1.0 \;m$. $A$ $100 \;kN$ force stretches it along its length. Calculate $(a)$ stress,$(b)$ elongation,and $(c)$ strain on the rod. Young's modulus of structural steel is $2.0 \times 10^{11} \;N \;m^{-2}$.

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Write the equation of bending in a rod. Write the unit of bending and its dimensional formula.

For a solid rod,the Young's modulus of elasticity is $3.2 \times 10^{11} \, N m^{-2}$ and density is $8 \times 10^3 \, kg m^{-3}$. The velocity of longitudinal wave in the rod will be $......... \times 10^{3} \, m s^{-1}$.

$A$ structural steel rod has a radius of $10 \;mm$ and a length of $1.0 \;m$. $A$ $100 \;kN$ force stretches it along its length. Calculate $(a)$ stress,$(b)$ elongation,and $(c)$ strain on the rod. Young's modulus of structural steel is $2.0 \times 10^{11} \;N \;m^{-2}$.

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