SATHEE: Properties of Matter 4 Question 1

Properties of Matter 4 Question 1

3. A man grows into a giant such that his linear dimensions increase by a factor of 9 . Assuming that his density remains same, the stress in the leg will change by a factor of

(2017 Main)

(a) $\frac{1}{9}$

(b) 81

(d) 9

Show Answer

Answer:

Correct Answer: 3. (a)

Solution:

By ascent formula, we have surface tension,

$\begin{aligned} T & = \frac{r h g}{2} \times 10^{3} \frac{N}{m} \\ = \frac{d h g}{4} \times 10^{3} \frac{N}{m} \end{aligned}$

$\begin{aligned} \Rightarrow \frac{Δ T}{T} = \frac{Δ d}{d} + \frac{Δ h}{h} [given, g is constant] \\ So, percentage = \frac{Δ T}{T} \times 100 = (\frac{Δ d}{d} + \frac{Δ h}{h}) \times 100 \end{aligned}$

$\begin{aligned} = (\frac{0.01 \times 10^{- 2}}{1.25 \times 10^{- 2}} + \frac{0.01 \times 10^{- 2}}{1.45 \times 10^{- 2}}) \times 100 \\ = 1.5 ∴ \frac{Δ T}{T} \times 100 & = 1.5 \end{aligned}$

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Properties of Matter 4 Question 1

3. A man grows into a giant such that his linear dimensions increase by a factor of 9 . Assuming that his density remains same, the stress in the leg will change by a factor of

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