The ratio of linear expansivity to the coeffi | vedclass

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

Question

(B) Let the length of the sides of a square sheet be $L$. The area of the sheet is $A = L^2$.When the temperature increases by $\Delta T$,the new leng

Vedclass · Accepted Answer

$0.5$

Vedclass · Answer

(B) Let the length of the sides of a square sheet be $L$. The area of the sheet is $A = L^2$.When the temperature increases by $\Delta T$,the new length becomes $L' = L(1 + \alpha \Delta T)$,where $\alpha$ is the coefficient of linear expansion.The new area becomes $A' = (L')^2 = L^2(1 + \alpha \Delta T)^2$.Expanding this,we get $A' = A(1 + 2\alpha \Delta T + \alpha^2 \Delta T^2)$.Since $\alpha$ is very small,$\alpha^2$ is negligible,so $A' \approx A(1 + 2\alpha \Delta T)$.The coefficient of superficial expansion $\beta$ is defined by the relation $A' = A(1 + \beta \Delta T)$.Comparing the two expressions,we find $\beta = 2\alpha$.Therefore,the ratio of linear expansivity $(\alpha)$ to the coefficient of superficial expansion $(\beta)$ is $\frac{\alpha}{\beta} = \frac{\alpha}{2\alpha} = 0.5$.

The ratio of linear expansivity to the coefficient of superficial expansion of a rectangular sheet of a solid is

Similar Questions

$A$ rod of length $10 \, m$ at $0 \, ^oC$ has a linear expansion coefficient $\alpha = (2x^2 + 1) \times 10^{-6} \, ^oC^{-1}$,where $x$ is the distance from one end of the rod. The length of the rod at $10 \, ^oC$ is: (in $, m$)

The temperature of a metal coin is increased by $100^{\circ} C$ and its diameter increases by $0.15 \%$. Its area increases by nearly (in $\%$)

To keep constant time,watches are fitted with a balance wheel made of:

$A$ pendulum clock loses $12 \ s$ a day if the temperature is $40^{\circ} C$ and gains $4 \ s$ a day if the temperature is $20^{\circ} C$. The temperature at which the clock will show the correct time is: (in $^{\circ} C$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module