If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a, b$ and $c$ respectively, then the corresponding ratio of increase in their lengths is
If the ratio of lengths, radii and Young's moduli of steel and brass wires in the figure are $a, b$ and $c$ respectively, then the corresponding ratio of increase in their lengths is
- [JEE MAIN 2013]
- A
$\frac{{3c}}{{2a{b^2}}}$
- B
$\frac{{2{a^2}c}}{b}$
- C
$\frac{{3a}}{{2{b^2}c}}$
- D
$\frac{{2ac}}{{{b^2}}}$
Similar Questions
A $0.1 \mathrm{~kg}$ mass is suspended from a wire of negligible mass. The length of the wire is $1 \mathrm{~m}$ and its crosssectional area is $4.9 \times 10^{-7} \mathrm{~m}^2$. If the mass is pulled a little in the vertically downward direction and released, it performs simple harmonic motion of angular frequency $140 \ \mathrm{rad} \mathrm{s}^{-1}$. If the Young's modulus of the material of the wire is $\mathrm{n} \times 10^9 \mathrm{Nm}^{-2}$, the value of $\mathrm{n}$ is
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- [IIT 2010]
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?
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One end of a metal wire is fixed to a ceiling and a load of $2 \mathrm{~kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1 \mathrm{~kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be____________.
[Area of cross section of wire $=0.005 \mathrm{~cm}^2$, $\mathrm{Y}=2 \times 10^{11}\ \mathrm{Nm}^{-2}$ and $\left.\mathrm{g}=10 \mathrm{~ms}^{-2}\right]$
One end of a metal wire is fixed to a ceiling and a load of $2 \mathrm{~kg}$ hangs from the other end. A similar wire is attached to the bottom of the load and another load of $1 \mathrm{~kg}$ hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be____________.
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- [JEE MAIN 2024]
Young's moduli of the material of wires $A$ and $B$ are in the ratio of $1: 4$, while its area of cross sections are in the ratio of $1: 3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $A$ and $B$ will be in the ratio of
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- [JEE MAIN 2023]