Four identical hollow cylindrical columns of | vedclass

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

Question

(D) Total mass $M = 50,000 \; kg$. Total force $F_{total} = Mg = 50,000 	imes 9.8 = 490,000 \; N$.Since there are $4$ columns,the force on each colum

Vedclass · Accepted Answer

$7.22 	imes 10^{-7}$

Vedclass · Answer

(D) Total mass $M = 50,000 \; kg$. Total force $F_{total} = Mg = 50,000 	imes 9.8 = 490,000 \; N$.Since there are $4$ columns,the force on each column is $F = \frac{490,000}{4} = 122,500 \; N$.The area of cross-section of each hollow column is $A = \pi(R^2 - r^2)$,where $R = 0.6 \; m$ and $r = 0.3 \; m$.$A = \pi(0.6^2 - 0.3^2) = \pi(0.36 - 0.09) = 0.27\pi \; m^2$.Stress on each column is $\sigma = \frac{F}{A} = \frac{122,500}{0.27\pi} \; Pa$.Using Young's modulus $Y = \frac{	ext{Stress}}{	ext{Strain}}$,the strain is $\epsilon = \frac{\sigma}{Y}$.Given $Y = 2.0 	imes 10^{11} \; Pa$,we have $\epsilon = \frac{122,500}{0.27 	imes \pi 	imes 2.0 	imes 10^{11}}$.$\epsilon = \frac{122,500}{1.69646 	imes 10^{11}} \approx 7.22 	imes 10^{-7}$.

Similar Questions

On increasing the length by $0.5\, mm$ in a steel wire of length $2\, m$ and area of cross-section $2\, mm^2$,the force required is ($Y$ for steel $= 2.2 \times 10^{11}\, N/m^2$).

$A$ metal rod of Young's modulus $Y$ and coefficient of thermal expansion $\alpha$ is held at its two ends such that its length remains invariant. If its temperature is raised by $t^{\circ} C$,the linear stress developed in it is

$A$ metallic ring of radius $r$ and cross-sectional area $A$ is fitted into a wooden circular disc of radius $R$ $(R > r)$. If the Young's modulus of the material of the ring is $Y$, the force with which the metal ring expands is

What is the Young's modulus and bulk modulus for a perfect rigid body?

Let $L$ be the length and $d$ be the diameter of the cross-section of a wire. Wires of the same material with different $L$ and $d$ are subjected to the same tension along the length of the wire. In which of the following cases will the extension of the wire be the maximum?

Vedclass Test Series

Exam Paper Generator

Online Exam Module