The following four wires of length L and radi | vedclass

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

Question

(A) The extension $\Delta \ell$ of a wire is given by the formula $\Delta \ell = \frac{F L}{A Y}$,where $F$ is the tension,$L$ is the length,$A$ is th

Vedclass · Accepted Answer

$L = 100 \ cm, r = 0.2 \ mm$

Vedclass · Answer

(A) The extension $\Delta \ell$ of a wire is given by the formula $\Delta \ell = \frac{F L}{A Y}$,where $F$ is the tension,$L$ is the length,$A$ is the cross-sectional area,and $Y$ is Young's modulus.Since $A = \pi r^2$,we have $\Delta \ell = \frac{F L}{\pi r^2 Y}$.Given that $F$ and $Y$ are constant for all wires,the extension $\Delta \ell$ is proportional to $\frac{L}{r^2}$.Calculating the ratio $\frac{L}{r^2}$ for each option:$A: \frac{100}{(0.2)^2} = \frac{100}{0.04} = 2500 \ cm/mm^2$$B: \frac{200}{(0.4)^2} = \frac{200}{0.16} = 1250 \ cm/mm^2$$C: \frac{300}{(0.6)^2} = \frac{300}{0.36} \approx 833.33 \ cm/mm^2$$D: \frac{400}{(0.8)^2} = \frac{400}{0.64} = 625 \ cm/mm^2$Comparing these values,the ratio is largest for option $A$.

The following four wires of length $L$ and radius $r$ are made of the same material. Which of these will have the largest extension,when the same tension is applied?

Similar Questions

$A$ galvanometer of resistance $G$ is connected in a circuit. Now,a resistance $R$ is connected in series with the galvanometer. To keep the main current in the circuit unchanged,the resistance $S$ to be put in parallel with the series combination of $G$ and $R$ is:

If $A = \begin{bmatrix} 0 & 2 \\ 3 & -4 \end{bmatrix}$ and $hA = \begin{bmatrix} 0 & 3a \\ 2b & 24 \end{bmatrix}$,then the values of $h, a, b$ are respectively

The energy $(E)$,angular momentum $(L)$,and universal gravitational constant $(G)$ are chosen as fundamental quantities. The dimensions of the universal gravitational constant in the dimensional formula of Planck's constant $(h)$ is

Which of the following electronic configurations would be associated with the highest magnetic moment?

Which hormone is responsible for apical dominance?

Vedclass Test Series

Exam Paper Generator

Online Exam Module