SATHEE: Properties of Matter 1 Question 3

Properties of Matter 1 Question 3

3. Young’s moduli of two wires $A$ and $B$ are in the ratio $7 : 4$ . Wire $A$ is $2 m$ long and has radius $R$ . Wire $B$ is $1.5 m$ long and has radius $2 m m$ . If the two wires stretch by the same length for a given load, then the value of $R$ is close to

(2019 Main, 8 April II)

(a) $1.3 m m$

(b) $1.5 m m$

(d) $1.7 m m$

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Answer:

Correct Answer: 3. (d)

Solution:

When a wire is stretched, then change in length of wire is $Δ l = \frac{F l}{π r^{2} Y}$ , where $Y$ is its Young’s modulus.

Here, for wires $A$ and $B$ ,

$\begin{aligned} l_{A} & = 2 m, l_{B} = 1.5 m \\ \frac{Y_{A}}{Y_{B}} & = \frac{7}{4}, r_{B} = 2 m m = 2 \times 10^{- 3} m and \frac{F_{A}}{F_{B}} = 1 \end{aligned}$

As, it is given that $Δ l_{A} = Δ l_{B}$

$\Rightarrow \frac{F_{A} l_{A}}{π r_{A}^{2} Y_{A}} = \frac{F_{B} l_{B}}{π r_{B}^{2} Y_{B}}$

$\Rightarrow r_{A}^{2} = \frac{F_{A}}{F_{B}} \cdot \frac{l_{A}}{l_{B}} \cdot \frac{Y_{B}}{Y_{A}} \cdot r_{B}^{2}$

$= 1 \times \frac{2}{1.5} \times \frac{4}{7} \times 4 \times 10^{- 6} m = 3.04 \times 10^{- 6} m$

or $r_{A} = 1.7 \times 10^{- 3} m$

or $r_{A} = 1.7 m m$

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Properties of Matter 1 Question 3

3. Young’s moduli of two wires $A$ and $B$ are in the ratio $7 : 4$ . Wire $A$ is $2 m$ long and has radius $R$ . Wire $B$ is $1.5 m$ long and has radius $2 m m$ . If the two wires stretch by the same length for a given load, then the value of $R$ is close to

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Properties of Matter 1 Question 3

3. Young’s moduli of two wires A and B are in the ratio 7:4. Wire A is 2m long and has radius R. Wire B is 1.5m long and has radius 2mm. If the two wires stretch by the same length for a given load, then the value of R is close to

Answer:

इंजीनियरिंग की तैयारी

चिकित्सा तैयारी

एनसीईआरटी पुस्तकें और समाधान

महत्वपूर्ण संसाधन

अन्य संसाधन

पाठ्यक्रम

परीक्षा मंच

नमूना मॉक टेस्ट

सदस्यता

एनसीईआरटी व्यायाम वीडियो समाधान

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3. Young’s moduli of two wires $A$ and $B$ are in the ratio $7 : 4$ . Wire $A$ is $2 m$ long and has radius $R$ . Wire $B$ is $1.5 m$ long and has radius $2 m m$ . If the two wires stretch by the same length for a given load, then the value of $R$ is close to