The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?
The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied ?
- A
Length $50\,cm$ and diameter $0.5\,mm$
- B
Length $100\,cm$ and diameter $1\,mm$
- C
Length $200\,cm$ and diameter $2\,mm$
- D
Length $300\,cm$ and diameter $3\,mm$
Similar Questions
$(a)$ A steel wire of mass $\mu $ per unit length with a circular cross section has a radius of $0.1\,cm$. The wire is of length $10\,m$ when measured lying horizontal and hangs from a hook on the wall. A mass of $25\, kg$ is hung from the free end of the wire. Assuming the wire to be uniform an lateral strains $< \,<$ longitudinal strains find the extension in the length of the wire. The density of steel is $7860\, kgm^{-3}$ and Young’s modulus $=2 \times 10^{11}\,Nm^{-2}$.
$(b)$ If the yield strength of steel is $2.5 \times 10^8\,Nm^{-2}$, what is the maximum weight that can be hung at the lower end of the wire ?
$(a)$ A steel wire of mass $\mu $ per unit length with a circular cross section has a radius of $0.1\,cm$. The wire is of length $10\,m$ when measured lying horizontal and hangs from a hook on the wall. A mass of $25\, kg$ is hung from the free end of the wire. Assuming the wire to be uniform an lateral strains $< \,<$ longitudinal strains find the extension in the length of the wire. The density of steel is $7860\, kgm^{-3}$ and Young’s modulus $=2 \times 10^{11}\,Nm^{-2}$.
$(b)$ If the yield strength of steel is $2.5 \times 10^8\,Nm^{-2}$, what is the maximum weight that can be hung at the lower end of the wire ?
An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is
An elastic material of Young's modulus $Y$ is subjected to a stress $S$. The elastic energy stored per unit volume of the material is
- [AIIMS 1997]
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