The following four wires are made of the same | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

Young's modulus,

$Y = \frac{{FL}}{{A\Delta L}} = \frac{{4FL}}{{\pi {D^2}\Delta L}}\,\,or\,\,\Delta L = \frac{{4FL}}{{\pi {D^2}Y}}$

Where $F$

Vedclass · Accepted Answer

length $ =50 \;cm$,diameter $=0.5\; mm$

Vedclass · Answer

Young's modulus,

$Y = \frac{{FL}}{{A\Delta L}} = \frac{{4FL}}{{\pi {D^2}\Delta L}}\,\,or\,\,\Delta L = \frac{{4FL}}{{\pi {D^2}Y}}$

Where $F$ is the force applied, $L$ is the length, $D$ is the diameter and $\Delta L$ is the extension of the wire respectively. 

As each wire is made up of same material therefore their $Young's$ modulus is same for each wire.

Foe all the four wires, $Y,F\,(=tension)$ are the same.

$	herefore \Delta L \propto \frac{L}{{{D^2}}}$

$In\,\,\left( a ight)\,\,\frac{L}{{{D^2}}} = \frac{{200\,cm}}{{{{\left( {0.2\,cm} ight)}^2}}} = 5 	imes {10^3}\,c{m^{ - 1}}$

$In\,\,\left( b ight)\,\,\,\frac{L}{{{D^2}}} = \frac{{300\,cm}}{{{{\left( {0.3\,cm} ight)}^2}}} = 3.3 	imes {10^3}\,c{m^{ - 1}}$

$In\,\,\left( c ight)\,\,\frac{L}{{{D^2}}} = \frac{{50\,cm}}{{{{\left( {0.05\,cm} ight)}^2}}} = 20 	imes {10^3}\,c{m^{ - 1}}$

$In\,\,\left( d ight)\,\,\frac{L}{{{D^2}}} = \frac{{100\,cm}}{{{{\left( {0.1\,cm} ight)}^2}}} = 10 	imes {10^3}\,\,c{m^{ - 1}}$

The following four wires are made of the same material. Which of these will have the largest extension when the same tension is applied?

Similar Questions

Two identical solid balls, one of ivory and the other of wet-clay are dropped from the same height on the floor. Which one will rise to a greater height after striking the floor and why ?

Four identical hollow cylindrical columns of mild steel support a big structure of mass $50,000 \;kg$. The inner and outer radii of each column are $30$ and $60\; cm$ respectively. Assuming the load distribution to be uniform, calculate the compressional strain of each column.

A uniform metallic wire is elongated by $0.04\, m$ when subjected to a linear force $F$. The elongation, if its length and diameter is doubled and subjected to the same force will be ..... $cm .$

A wire is stretched by $0.01$ $m$ by a certain force $F.$ Another wire of same material whose diameter and length are double to the original wire is stretched by the same force. Then its elongation will be