SATHEE: Mechanical Properties of Solids

Mechanical Properties of Solids - Result Question 6

7. If the ratio of diameters, lengths and Young’s modulus of steel and copper wires shown in the figure are $p, q$ and $s$ respectively, then the corresponding ratio of increase in their lengths would be

[NEET Kar: 2013]

(a) $\frac{7 q}{(5 s p)}$

(b) $\frac{5 q}{(7 s p^{2})}$

(d) $\frac{2 q}{(5 s p)}$

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Answer:

Correct Answer: 7. (c)

Solution:

Increase in length $Δ L = \frac{F L}{A Y} = \frac{4 F L}{π D^{2} Y}$

$\begin{aligned} \frac{Δ L_{S}}{Δ L_{C}} & = \frac{F_{S}}{F_{C}} (\frac{D_{C}}{D_{S}})^{2} \frac{Y_{C}}{Y_{S}} \frac{L_{S}}{L_{C}} = \frac{7}{5} \times (\frac{1}{p})^{2} (\frac{1}{s}) q \\ = \frac{7 q}{(5 s p^{2})} \end{aligned}$

If a wire of length $l$ is suspended from a rigid support and $A$ is the area of cross-section of the wire, then mass of the wire, $m = A l p$ . Then extension in the wire due to its own weight can be find as follows.

Young Modulus, $Y = \frac{m g}{A} \times \frac{(l / 2)}{Δ l}$

Here, $L = l / 2$ because the weight of wire acts at the mid point of wire.

$∴$ Extension in the wire due to its own weight $Δ l = \frac{l^{2} p g}{2 Y}$

Mechanical Properties of Solids - Result Question 6

7. If the ratio of diameters, lengths and Young’s modulus of steel and copper wires shown in the figure are $p, q$ and $s$ respectively, then the corresponding ratio of increase in their lengths would be

Answer:

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Mechanical Properties of Solids - Result Question 6

7. If the ratio of diameters, lengths and Young’s modulus of steel and copper wires shown in the figure are p,q and s respectively, then the corresponding ratio of increase in their lengths would be

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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7. If the ratio of diameters, lengths and Young’s modulus of steel and copper wires shown in the figure are $p, q$ and $s$ respectively, then the corresponding ratio of increase in their lengths would be