(A) The breaking tension force for the wire is given by $F = \sigma \cdot A$. Substituting the given values: $F = (4.8 \times 10^7 \ N \ m^{-2}) \time

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(A) The breaking tension force for the wire is given by $F = \sigma \cdot A$. Substituting the given values: $F = (4.8 \times 10^7 \ N \ m^{-2}) \times (10^{-6} \ m^2) = 48 \ N$. This tension force provides the necessary centripetal force for the body to rotate in a horizontal circle: $F_C = m \omega^2 r = 48 \ N$. Given $m = 10 \ kg$ and $r = 0.3 \ m$,we have $10 \times \omega^2 \times 0.3 = 48$. $3 \omega^2 = 48 \Rightarrow \omega^2 = 16$. Therefore,$\omega = 4 \ rad \ s^{-1}$.

Class 11 Physics Mechanical Properties of Solids Mix Examples-Mechanical Properties of Solids

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$A$ body of mass $10 \ kg$ is attached to a wire of $0.3 \ m$ length. The breaking stress is $4.8 \times 10^7 \ N \ m^{-2}$. The area of cross-section of the wire is $10^{-6} \ m^2$. The maximum angular velocity with which it can be rotated in a horizontal circle is

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A
$4 \ rad \ s^{-1}$
B
$8 \ rad \ s^{-1}$
C
$16 \ rad \ s^{-1}$
D
$32 \ rad \ s^{-1}$

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Mix Examples-Mechanical Properties of Solids

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Which of the following statements is incorrect?

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Write the formula,dimensional formula,and $SI$ unit for the Shear Modulus and the Bulk Modulus.

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Two identical steel cubes (masses $50\,g$,side $1\,cm$) collide head-on face to face with a speed of $10\,cm/s$ each. Find the maximum compression of each. Young's modulus for steel $Y = 2 \times 10^{11}\,N/m^2$.

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$A$ body of mass $10 \ kg$ is attached to a wire of $0.3 \ m$ length. The breaking stress is $4.8 \times 10^7 \ N \ m^{-2}$. The area of cross-section of the wire is $10^{-6} \ m^2$. The maximum angular velocity with which it can be rotated in a horizontal circle is

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Which of the following statements is incorrect?

$A$ wire of density $3 \times 10^3 \, kg/m^3$ requires a breaking stress of $10^6 \, N/m^2$ to break. What should be the length of the wire so that it breaks under its own weight? (Take $g = 10 \, m/s^2$)

Write the formula,dimensional formula,and $SI$ unit for the Shear Modulus and the Bulk Modulus.

Two identical steel cubes (masses $50\,g$,side $1\,cm$) collide head-on face to face with a speed of $10\,cm/s$ each. Find the maximum compression of each. Young's modulus for steel $Y = 2 \times 10^{11}\,N/m^2$.

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