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Chapter 7: Problem 1000

The excess of pressure inside a soap bubble than that of the outer pressure is (A) \((2 \mathrm{~T} / \mathrm{r})\) (B) \((4 \mathrm{~T} / \mathrm{r})\) (C) \((\mathrm{T} / 2 \mathrm{r})\) (D) \((\mathrm{T} / \mathrm{r})\)

Short Answer

Expert verified
The correct answer is (B) \((4 \mathrm{~T} / \mathrm{r})\), as it matches the formula for excess pressure inside a soap bubble given by the Young-Laplace equation: \(\Delta P = \frac{4 \mathrm{~T}}{\mathrm{r}}\).

Step by step solution

01

Option A - \((2 \mathrm{~T} / \mathrm{r})\)

From the Young-Laplace equation, the excess pressure inside a soap bubble can be calculated using the formula: \(\Delta P = \frac{4 \mathrm{~T}}{\mathrm{r}}\) Comparing this formula with the given option, we can see that Option A is not correct because it includes a factor of 2 instead of a factor of 4 in the numerator.
02

Option B - \((4 \mathrm{~T} / \mathrm{r})\)

As mentioned earlier, the Young-Laplace equation provides the formula for the excess pressure inside a soap bubble: \(\Delta P = \frac{4 \mathrm{~T}}{\mathrm{r}}\) Comparing this formula with the given option, we can see that Option B is the correct answer.
03

Option C - \((\mathrm{T} / 2 \mathrm{r})\)

Comparing the Young-Laplace equation \(\Delta P = \frac{4 \mathrm{~T}}{\mathrm{r}}\) with Option C, we find that this option contains a 1/2 factor instead of a 4 factor on top. This indicates that Option C is incorrect.
04

Option D - \((\mathrm{T} / \mathrm{r})\)

Comparing the Young-Laplace equation \(\Delta P = \frac{4 \mathrm{~T}}{\mathrm{r}}\) with Option D, we find that this option contains a factor of 1 instead of a factor of 4 in the numerator. This indicates that Option D is also incorrect. From our analysis, we find that the correct answer is: (B) \((4 \mathrm{~T} / \mathrm{r})\)

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Most popular questions from this chapter

A rubber ball when taken to the bottom of a \(100 \mathrm{~m}\) deep take decrease in volume by \(1 \%\) Hence, the bulk modulus of rubber is $\ldots \ldots \ldots . . .\left[\mathrm{g}=10\left(\mathrm{~m} / \mathrm{s}^{2}\right)\right]$ (A) \(10^{6} \mathrm{~Pa}\) (B) \(10^{8} \mathrm{~Pa}\) (C) \(10^{7} \mathrm{~Pa}\) (D) \(10^{9} \mathrm{~Pa}\)

What is the possible value of posson's ratio? (A) 1 (B) \(0.9\) (C) \(0.8\) (D) \(0.4\)

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) \(3 \times 10^{10}\left(\mathrm{~N} / \mathrm{m}^{2}\right)\)

For a constant hydraulic stress on an object, the fractional change in the object volume \([\Delta \mathrm{V} / \mathrm{V}]\) and its bulk modulus (B) are related as............ (A) \((\Delta \mathrm{V} / \mathrm{V}) \alpha \beta\) (B) \((\Delta \mathrm{V} / \mathrm{V}) \alpha \beta^{-1}\) (C) \((\Delta \mathrm{V} / \mathrm{V}) \alpha \beta^{2}\) (D) \((\Delta \mathrm{V} / \mathrm{V}) \alpha \beta^{-2}\)

A material has poisson's ratio \(0.50\). If uniform rod of it suffers longitudinal strain of \(2 \times 10^{-3}\). Then what is percentage change in volume ? (A) \(0.6\) (B) \(0.4\) (C) \(0.2\) (D) 0
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