Q134 / 160 · AP EAMCET 2022 (06 Jul Shift 2) · Physics
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.
- AA, B and C are true.
- B$A, B$ are true $C$ is false.
- Correct answerC$A, C$ are true $B$ is false.
- D$\mathrm{B}$ 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.
Hence, the correct answer is option: 'C'.