A cylindrical rod made of aluminum has a leng | vedclass

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

Question

(D) Given: Length $l = 1 \,m$, Diameter $d = 10 \,cm = 0.1 \,m$, Radius $r = 0.05 \,m$, Force $F = 100 \,kN = 10^5 \,N$, Young's modulus $Y = 70 \,GPa

Vedclass · Accepted Answer

$1.81 	imes 10^{-4} \,m$

Vedclass · Answer

(D) Given: Length $l = 1 \,m$, Diameter $d = 10 \,cm = 0.1 \,m$, Radius $r = 0.05 \,m$, Force $F = 100 \,kN = 10^5 \,N$, Young's modulus $Y = 70 \,GPa = 70 	imes 10^9 \,Pa$.Using the formula for Young's modulus: $Y = \frac{F \cdot l}{A \cdot \Delta l}$, where $A = \pi r^2$.Rearranging for elongation $\Delta l$: $\Delta l = \frac{F \cdot l}{\pi r^2 Y}$.Substituting the values: $\Delta l = \frac{10^5 	imes 1}{3.14159 	imes (0.05)^2 	imes 70 	imes 10^9}$.$\Delta l = \frac{10^5}{3.14159 	imes 0.0025 	imes 70 	imes 10^9} = \frac{10^5}{549.78 	imes 10^6} \approx 1.81 	imes 10^{-4} \,m$.

$A$ cylindrical rod made of aluminum has a length of $1 \,m$ and a diameter of $10 \,cm$. The rod is subjected to a tensile force of $100 \,kN$. Calculate the elongation in the rod. (Young's modulus of aluminum $= 70 \,GPa$)

Similar Questions

Which of the following graphs correctly depicts the spring constant $k$ versus the length $l$ of the spring?

Four wires of the same material are stretched by the same load. Which one of them will elongate the most if their dimensions are as follows?

Two wires $A$ and $B$ are stretched by the same force. If,for $A$ and $B$,$Y_A: Y_B = 1: 2$,$r_A: r_B = 3: 1$,and $L_A: L_B = 4: 1$,then the ratio of their extension $\left(\frac{\Delta L_A}{\Delta L_B}\right)$ will be .............

If $\rho$ is the density of the material of a wire and $\sigma$ is the breaking stress, what is the greatest length of the wire that can hang freely without breaking?

$A$ wire extends by $1 \ mm$ when a force is applied. If double the force is applied to another wire of the same material and length but half the radius of the cross-section,what will be the elongation of the wire in $mm$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module