SATHEE: Properties of Matter 1 Question 6

Properties of Matter 1 Question 6

6. A load of mass $M k g$ is suspended from a steel wire of length $2 m$ and radius $1.0 m m$ in Searle’s apparatus experiment. The increase in length produced in the wire is $4.0 m m$ . Now, the load is fully immersed in a liquid of relative density 2 . The relative density of the material of load is 8 . The new value of increase in length of the steel wire is

(2019 Main, 12 Jan II)

(a) zero

(b) $5.0 m m$

(d) $3.0 m m$

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Answer:

Correct Answer: 6. (d)

Solution:

When load $M$ is attached to wire, extension in length of wire is

$Δ l_{1} = \frac{M g l}{A . Y}$

where, $Y$ is the Young’s modulus of the wire.

when load is immersed in liquid of relative density 2, increase in length of wire as shown in the figure is

$Δ l_{2} = \frac{(M g - F_{B}) l}{A . Y}$

where, $F_{B} =$ Buoyant force

$∴ Δ l_{2} = \frac{(M g - M g \cdot \frac{ρ_{l}}{ρ_{b}}) l}{A . Y} [∵ F_{B} = V ρ_{l} g = \frac{M g}{ρ_{b}} ρ_{l} g]$

Here given that, $\frac{ρ_{l}}{ρ_{b}} = \frac{2}{8} = \frac{1}{4}$

So, $Δ l_{2} = \frac{(\frac{3}{4} M g) l}{A . Y}$

Dividing Eqs. (ii) by (i), we get

$\Rightarrow \begin{aligned} \frac{Δ l_{2}}{Δ l_{1}} & = \frac{3}{4} \\ Δ l_{2} & = \frac{3}{4} \times Δ l_{1} \\ = \frac{3}{4} \times 4 m m = 3 m m \end{aligned}$

204 Properties of Matter

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Properties of Matter 1 Question 6

Answer:

204 Properties of Matter

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Properties of Matter 1 Question 6

Answer:

204 Properties of Matter

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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