Bending ? How bending problems prevents and buckling ?

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8.Mechanical Properties of Solids

hard

What is bending ? How bending problems prevents and what is buckling ?

Option A

Option B

Option C

Option D

Solution

A bridge has to be designed such that it can withstand the load of the flowing traffic, the force of winds and its own weight. Means it should not bend too much or break.

Similarly, in the design of building use of beams and column is very common.

In both the cases, the overcoming of the problem of bending of beam under a load is important.

Let us consider the case of a beam loaded at the centre and supported near its ends as shown in figure $(a)$.

A bar of length $l$, breadth $b$ and depth $d$ when loaded at the centre by a load $\mathrm{W}$ sags by an amount given by,

$\delta=\frac{\mathrm{W} l^{3}}{4 b d^{3} \mathrm{Y}}$

where $\mathrm{Y}=$ Young modulus

This equation shows that,

Bending $\delta \propto \frac{l^{3}}{b d^{3} \mathrm{Y}}$

Means for reduce the bending for the given load, the distance between two support must be small or one should use a material of beam with large Young's modulus.

Standard 11

Physics

The extension of a wire by the application of load is $3$ $mm.$ The extension in a wire of the same material and length but half the radius by the same load is….. $mm$

medium

A load of $2 \,kg$ produces an extension of $1 \,mm$ in a wire of $3 \,m$ in length and $1 \,mm$ in diameter. The Young's modulus of wire will be ………. $Nm ^{-2}$

easy

A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length increases by $l$. Another wire of same material of length $2 L$ and radius $2 r$ is pulled by a force $2 f$. Then the increase in its length will be

medium

(JEE MAIN-2023)

A brass rod of length $2\,m$ and cross-sectional area $2.0\,cm^2$ is attached end to end to a steel rod of length $L$ and cross-sectional area $1.0\,cm^2$ . The compound rod is subjected to equal and opposite pulls of magnitude $5 \times 10^4\,N$ at its ends. If the elongations of the two rods are equal, then length of the steel rod $(L)$ is ……….. $m$ $(Y_{Brass}=1.0\times 10^{11}\,N/m^2$ and $Y_{Steel} = 2.0 \times 10^{11}\,N/m^2)$

medium

The length of an iron wire is $L$ and area of cross-section is $A$. The increase in length is $l$ on applying the force $F$ on its two ends. Which of the statement is correct

easy

What is bending ? How bending problems prevents and what is buckling ?

Solution

Similar Questions

The extension of a wire by the application of load is $3$ $mm.$ The extension in a wire of the same material and length but half the radius by the same load is….. $mm$

A load of $2 \,kg$ produces an extension of $1 \,mm$ in a wire of $3 \,m$ in length and $1 \,mm$ in diameter. The Young's modulus of wire will be ………. $Nm ^{-2}$

A wire of length $L$ and radius $r$ is clamped rigidly at one end. When the other end of the wire is pulled by a force $f$, its length increases by $l$. Another wire of same material of length $2 L$ and radius $2 r$ is pulled by a force $2 f$. Then the increase in its length will be

The length of an iron wire is $L$ and area of cross-section is $A$. The increase in length is $l$ on applying the force $F$ on its two ends. Which of the statement is correct

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