The pressure to be applied to the ends of a s | vedclass

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

Question

(A) The thermal stress required to prevent expansion is equal to the pressure applied.Thermal stress is given by the formula: $\sigma = Y 	imes 	ext

Vedclass · Accepted Answer

$0.22 	imes 10^9 	ext{ Pa}$

Vedclass · Answer

(A) The thermal stress required to prevent expansion is equal to the pressure applied.Thermal stress is given by the formula: $\sigma = Y 	imes 	ext{thermal strain}$.Thermal strain is defined as $\frac{\Delta L}{L} = \alpha \Delta T$.Therefore, the pressure $P$ is given by $P = Y \alpha \Delta T$.Given values:$Y = 200 	ext{ GPa} = 200 	imes 10^9 	ext{ Pa}$$\alpha = 11 	imes 10^{-6} / K$$\Delta T = 100^{\circ} C = 100 	ext{ K}$Substituting these values into the formula:$P = (200 	imes 10^9) 	imes (11 	imes 10^{-6}) 	imes 100$$P = 200 	imes 11 	imes 10^9 	imes 10^{-6} 	imes 10^2$$P = 2200 	imes 10^5 = 2.2 	imes 10^8 	ext{ Pa} = 0.22 	imes 10^9 	ext{ Pa}$.

The pressure to be applied to the ends of a steel cylinder to keep its length constant upon raising its temperature by $100^{\circ} C$ is (thermal expansion coefficient, $\alpha = 11 \times 10^{-6} / K$, Young's modulus $Y = 200 \text{ GPa}$)

Similar Questions

$5 \,m$ long aluminium wire $(Y = 7 \times 10^{10} \,N/m^2)$ of diameter $3 \,mm$ supports a $40 \,kg$ mass. In order to have the same elongation in a copper wire $(Y = 12 \times 10^{10} \,N/m^2)$ of the same length under the same weight, the diameter should be (in $mm$):

$A$ steel rod with a circular cross-section of diameter $1 \ cm$ and another steel rod with a square cross-section of side $1 \ cm$ have equal mass. If the two rods are subjected to the same tension, the ratio of the elongations of the two rods is

The following four wires are made of the same material. Which one will have the largest elongation when subjected to the same tension?

$A$ steel wire of $1 \, m$ long and $1 \, mm^2$ cross-sectional area is hung from a rigid support. When a weight of $1 \, kg$ is hung from it,the change in length will be given by ..... $mm$ $(Y = 2 \times 10^{11} \, N/m^2, g = 10 \, m/s^2)$.

The stress versus strain graphs for wires of two materials $A$ and $B$ are as shown in the figure. If $Y_A$ and $Y_B$ are the Young's modulus of the materials,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module