A solid rectangular sheet has two different c | vedclass

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

Question

(D) Let the initial length be $L_{0}$ and initial breadth be $B_{0}$. The initial area is $S_{0} = L_{0} B_{0}$.When the temperature increases by $\De

Vedclass · Accepted Answer

$\alpha_{1}+\alpha_{2}$

Vedclass · Answer

(D) Let the initial length be $L_{0}$ and initial breadth be $B_{0}$. The initial area is $S_{0} = L_{0} B_{0}$.When the temperature increases by $\Delta t$,the new length $L_{t}$ and new breadth $B_{t}$ are given by:$L_{t} = L_{0}(1 + \alpha_{1} \Delta t)$$B_{t} = B_{0}(1 + \alpha_{2} \Delta t)$The new area $S_{t}$ is:$S_{t} = L_{t} 	imes B_{t} = L_{0}(1 + \alpha_{1} \Delta t) 	imes B_{0}(1 + \alpha_{2} \Delta t)$$S_{t} = L_{0} B_{0} (1 + \alpha_{1} \Delta t + \alpha_{2} \Delta t + \alpha_{1} \alpha_{2} (\Delta t)^{2})$Since $\alpha_{1} \Delta t \ll 1$ and $\alpha_{2} \Delta t \ll 1$,the term $\alpha_{1} \alpha_{2} (\Delta t)^{2}$ is negligible.$S_{t} \approx S_{0} (1 + (\alpha_{1} + \alpha_{2}) \Delta t)$Comparing this with the standard formula for surface expansion $S_{t} = S_{0} (1 + \beta \Delta t)$,where $\beta$ is the coefficient of surface expansion:$\beta = \alpha_{1} + \alpha_{2}$

$A$ solid rectangular sheet has two different coefficients of linear expansion $\alpha_{1}$ and $\alpha_{2}$ along its length and breadth respectively. The coefficient of surface expansion is (for $\alpha_{1} \Delta t \ll 1, \alpha_{2} \Delta t \ll 1$):

Similar Questions

$A$ steel scale measures the length of a copper wire as $80.0\,cm$ when both are at $20^\circ C$ (the calibration temperature for the scale). What would be the scale reading for the length of the wire when both are at $40^\circ C$ (in $,cm$)?

The rods of length $L_1$ and $L_2$ are made of materials whose coefficients of linear expansion are $\alpha_1$ and $\alpha_2$ respectively. If the difference between the two lengths is independent of temperature,then:

$A$ pendulum clock shows the correct time at $20\,^oC$. The coefficient of linear expansion of the pendulum material is $12 \times 10^{-6}\,^oC^{-1}$. How much time in $sec/day$ will it lose at $40\,^oC$?

The coefficient of linear expansion depends on

$A$ 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