Explain experimental determination of Young’s modulus.
Explain experimental determination of Young’s modulus.
A typical experimental arrangement to determine Young's modulus of a material of wire is shown as in figure.
It consists of two long straight wires of same length and equal radius suspended side by side from a fixed rigid support.
The wire$ A$ (reference wire) carries a millimeter main scale M and a pan to place a weight. The wire $B$ (experimental wire) of uniform area of cross-section also carries a pan in which known weights can be placed.
A vernier scale $\mathrm{V}$ is attached to a pointer at the bottom of the experimental wire $\mathrm{B}$ and the main scale $M$ is fixed to the reference wire $A$.
The weights placed in the pan exert a downward force and stretch the experimental wire under a tensile stress. The elongation of the wire is measured by the vernier arrangement. The reference wire is used to compensate for any change in length that may occur due to change in room temperature, any change in length of the reference wire will be accompanied by an equal change in experimental wire.
Both the reference and experimental wires are given an initial small load to keep the wires straight and the vernier reading is noted.
Now the experimental wire is gradually loaded with more weights to bring it under a tensile stress and the vernier reading is noted again.
The difference between two vernier readings gives the elongation produced in the wire.
Let $r$ and $\mathrm{L}$ be the initial radius and length of the experimental wire respectively then the area of cross-section of wire would be $\pi r^{2}$.
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If Young's modulus of iron is $2 \times {10^{11}}\,N/{m^2}$ and the interatomic spacing between two molecules is $3 \times {10^{ - 10}}$metre, the interatomic force constant is ......... $N/m$
If Young's modulus of iron is $2 \times {10^{11}}\,N/{m^2}$ and the interatomic spacing between two molecules is $3 \times {10^{ - 10}}$metre, the interatomic force constant is ......... $N/m$
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
[Assume length of wires $A$ and $B$ are same]
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
[Assume length of wires $A$ and $B$ are same]
- [JEE MAIN 2023]
Wires $A$ and $B$ are connected with blocks $P$ and $Q$ as shown. The ratio of lengths, radii and Young's modulus of wires $A$ and $B$ are $r, 2r$ and $3r$ respectively ($r$ is a constant). Find the mass of block $P$ if ratio of increase in their corresponding lengths is $1/6r^2$. The mass of block $Q$ is $3M$.
Wires $A$ and $B$ are connected with blocks $P$ and $Q$ as shown. The ratio of lengths, radii and Young's modulus of wires $A$ and $B$ are $r, 2r$ and $3r$ respectively ($r$ is a constant). Find the mass of block $P$ if ratio of increase in their corresponding lengths is $1/6r^2$. The mass of block $Q$ is $3M$.
A composite rod made up of two rods $AB$ and $BC$ are joined at $B$ . The rods are of equal length at room temperature and have equal masses. The coefficient of linear expansion a of $AB$ is more than that of $BC$. The composite rod is suspended horizontal by means of a thread at $B$. When the rod is heated
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