Statement (A) For an ideal liquid, the bulk modulus is infinite and the shear modulus is zero. Statement (B)…

Statement (A) For an ideal liquid, the bulk modulus is infinite and the shear modulus is zero. Statement (B) The volume contraction of a metal cube of bulk modulus $140 \mathrm{GPa} .10 \mathrm{~cm}$ on a edge, when subjected to a hydraulic pressure of $7 \times 10^6 \mathrm{~Pa}$ is $-0.05 \mathrm{~m}^3$. Statement (C) A spiral spring is stretched by a weight attached to it. The strain is tensile.
  1. A, B and C are true.
  2. $A, B$ are true $C$ is false.
  3. $A, C$ are true $B$ is false.
  4. $\mathrm{B}$ and $\mathrm{C}$ are true $\mathrm{A}$ is false.

Solution

For an ideal liquid, the bulk modulus, is infinite and shear modulus is zero. Hence, statement (A) is correct. In statement (B), Bulk modulus $ \begin{aligned} B & =140 \mathrm{GPa} \\ & =140 \times 10^9 \mathrm{~Pa} \\ & =1.4 \times 10^{11} \mathrm{~Pa} \\ p & =7 \times 10^6 \mathrm{~Pa} \\ V & =a^3=(0.1)^3 \\ & =0.001 \mathrm{~m}^3 \end{aligned} $ $ [a=10 \mathrm{~cm}=0.1 \mathrm{~m}] $ since, $\quad B=\frac{p}{\left(\frac{-\Delta V}{V}\right)}$ $ \begin{aligned} & \Rightarrow 1.4 \times 10^{11}=\frac{7 \times 10^6}{\frac{-\Delta V}{0.001}} \\ & \Rightarrow 1.4 \times 10^{11}=\frac{7 \times 10^3}{-\Delta V} \end{aligned} $ $ \Rightarrow 1.4 \times 10^{11}=\frac{7 \times 10^3}{-\Delta V} $ $ \begin{aligned} \Rightarrow \quad \Delta V & =-\frac{7 \times 10^3}{1.4 \times 10^{11}} \\ & =-5 \times 10^{-8} \mathrm{~m}^3 \end{aligned} $ Hence, statement (B) is incorrect. Strain produced in spiral spring stretched by a weight attached to it, is tensile. Hence, statement $(C)$ is correct

Asked in: AP EAMCET 2022 (06 Jul Shift 2)

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