SATHEE: Properties of Matter 4 Question 3

Properties of Matter 4 Question 3

5. The pressure that has to be applied to the ends of a steel wire of length $10 c m$ to keep its length constant when its temperature is raised by $100^{\circ} C$ is (For steel, Young’s modulus is $2 \times 10^{11} N m^{- 2}$ and coefficient of thermal expansion is $1.1 \times 10^{- 5} K^{- 1}$ )

(2014 Main)

(a) $2.2 \times 10^{8} P a$

(b) $2.2 \times 10^{9} P a$

(d) $2.2 \times 10^{6} P a$

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Answer:

Correct Answer: 5. (*)

Solution:

The bubble will detach if,

$\int \sin θ T \times d l = T (2 π r) \sin θ$

Buoyant force $\geq$ Surface tension force

$\begin{aligned} \frac{4}{3} π R^{3} ρ_{w} g & \geq \int T \times d l \sin θ \\ (ρ_{w}) (\frac{4}{3} π R^{3}) g & \geq (T) (2 π r) \sin θ \\ \sin θ & = \frac{r}{R} \end{aligned}$

Solving, $r = \sqrt{\frac{2 ρ_{w} R^{4} g}{3 T}} = R^{2} \sqrt{\frac{2 ρ_{w} g}{3 T}}$

No option matches with the correct answer.

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Properties of Matter 4 Question 3

5. The pressure that has to be applied to the ends of a steel wire of length 10cm to keep its length constant when its temperature is raised by 100∘C is (For steel, Young’s modulus is 2×1011Nm−2 and coefficient of thermal expansion is 1.1×10−5K−1 )

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