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Chapter 7: Problem 971

When \(100 \mathrm{~N}\) tensile force is applied to a rod of $10^{-6} \mathrm{~m}^{2}\( cross-sectional area, its length increases by \)1 \%$ so young's modulus of material is \(\ldots \ldots \ldots \ldots\) (A) \(10^{12} \mathrm{~Pa}\) (B) \(10^{11} \mathrm{~Pa}\) (C) \(10^{10} \mathrm{~Pa}\) (D) \(10^{2} \mathrm{~Pa}\)

Short Answer

Expert verified
The Young's modulus of the material is \(10^{10} \mathrm{~Pa}\).

Step by step solution

01

Find the change in length ΔL

We are given that the length increases by 1% when a tensile force is applied. So, ΔL = L0 × 0.01
02

Rearrange the formula for Young's modulus

Young's modulus (Y) = (Tensile force (F) × Original length(L0)) / (Area (A) × Change in length (ΔL))
03

Substitute the values into the formula

Substitute the values given in the problem: Tensile force (F) = 100 N, Area (A) = 10^{-6} m², and the change in length (ΔL) = L0 × 0.01 into the formula: Y = (100 × L0) / (10^{-6} × L0 × 0.01) You can notice that 'L0' on the numerator and denominator can be canceled out.
04

Simplify the formula

After canceling out L0, we have: Y = (100) / ( 10^{-6} × 0.01) Now, let's simplify: Y = (100) / (10^{-8}) Y = 100 × 10^{8} Y = 10^{10} Pa So, the Young's modulus of the material is \(10^{10} \mathrm{~Pa}\). The correct answer is option (C).

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Most popular questions from this chapter

The density \(\rho\) of coater of bulk modulus \(B\) at a depth \(y\) in the ocean is related to the density at surface \(\rho_{0}\) by the relation. (A) $\rho=\rho_{0}\left[1-\left\\{\left(\rho_{0} \mathrm{gy}\right\\} / \mathrm{B}\right\\}\right]$ (B) $\rho=\rho_{0}\left[1+\left\\{\left(\rho_{0} \mathrm{gy}\right\\} / \mathrm{B}\right\\}\right]$ (C) $\rho=\rho_{0}\left[1+\left\\{\left(\rho_{0} \mathrm{gyh}\right\\} / \mathrm{B}\right\\}\right]$ (D) $\rho=\rho_{0}\left[1-\left\\{\mathrm{B} /\left(\rho_{0} \mathrm{~g} \mathrm{y}\right\\}\right]\right.$

Read the assertion and reason carefully to mark the correct option out of the option given below. (a) If both assertion and reason are true and the reason is the correct explanation of the reason. (b) If both assertion and reason are true but reason is not the correct explanation of the assertion. (c) If assertion is true but reason is false. (d) If the assertion and reason both are false. (e) If assertion is false but reason is true. Assertion: The molecules of \(0^{\circ} \mathrm{C}\) ice and $0^{\circ} \mathrm{C}$ water will have same potential energy. Reason: Potential energy depends only on temperature of the system. (A) a (B) \(b\) (C) \(\mathrm{c}\) (D) d (E) e

If the young's modulus of the material is 3 times its modulus of rigidity. Then what will be its volume elasticity? (A) zero (B) infinity (C) \(2 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\) (D) \(3 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

What is the ratio of the adiabatic to isothermal elasticities of a triatomic gas ? (A) \((3 / 4)\) (B) \((4 / 3)\) (C) 1 (D) \((5 / 3)\)

The force required to separate two glass plates of area $10^{-2} \mathrm{~m}^{2}\( with a film of water \)0.05 \mathrm{~mm}$ thick between them is (surface tension of water is \(70 \times 10^{-3} \mathrm{~N} / \mathrm{m}\) ) (A) \(28 \mathrm{~N}\) (B) \(14 \mathrm{~N}\) (C) \(50 \mathrm{~N}\) (D) \(38 \mathrm{~N}\)
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