A metallic bar of Young's modulus 0.5 times 1 | vedclass

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

Question

(A) The thermal strain produced in the bar is given by $\epsilon = \alpha \Delta T$.Given $\alpha = 10^{-5} \,^{\circ}C^{-1}$ and $\Delta T = 100^{\ci

Vedclass · Accepted Answer

$50 	imes 10^3 \,N$

Vedclass · Answer

(A) The thermal strain produced in the bar is given by $\epsilon = \alpha \Delta T$.Given $\alpha = 10^{-5} \,^{\circ}C^{-1}$ and $\Delta T = 100^{\circ}C - 0^{\circ}C = 100^{\circ}C$.So, $\epsilon = 10^{-5} 	imes 100 = 10^{-3}$.Since the bar is prevented from expanding, the compressive stress $\sigma$ is given by $\sigma = Y 	imes \epsilon$, where $Y$ is Young's modulus.$\sigma = (0.5 	imes 10^{11} \,N \,m^{-2}) 	imes 10^{-3} = 0.5 	imes 10^8 \,N \,m^{-2}$.The compressive force $F$ is given by $F = \sigma 	imes A$, where $A$ is the area of cross-section.$F = (0.5 	imes 10^8 \,N \,m^{-2}) 	imes (10^{-3} \,m^2) = 0.5 	imes 10^5 \,N = 50 	imes 10^3 \,N$.

Similar Questions

If the ratio of diameters,lengths and Young's moduli of steel and brass wires shown in the figure are $p, q$ and $r$ respectively,then the corresponding ratio of increase in their lengths would be

Which coefficient of elasticity is responsible for the propagation of a wave in a string?

$A$ load $W$ produces an extension of $1 \ mm$ in a thread of radius $r$. If the load is increased to $4W$ and the radius is increased to $2r$,while all other factors remain the same,what will be the new extension in $mm$?

Increase in length of a wire is $1 \, mm$ when suspended by a weight. If the same weight is suspended on a wire of double its length and double its radius,the increase in length will be ........ $mm$.

For a solid rod,the Young's modulus of elasticity is $3.2 \times 10^{11} \, N m^{-2}$ and density is $8 \times 10^3 \, kg m^{-3}$. The velocity of longitudinal wave in the rod will be $......... \times 10^{3} \, m s^{-1}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module