The difference in length between two rods A a | vedclass

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

Question

(B) Given: The difference in length $\Delta l = l_{A} - l_{B} = 60 	ext{ cm}$ is constant at all temperatures.This implies that the change in length

Vedclass · Accepted Answer

$l_{A} = 180 	ext{ cm}, l_{B} = 120 	ext{ cm}$

Vedclass · Answer

(B) Given: The difference in length $\Delta l = l_{A} - l_{B} = 60 	ext{ cm}$ is constant at all temperatures.This implies that the change in length for both rods must be equal for any temperature change $\Delta T$.$\Delta l_{A} = \Delta l_{B}$$l_{A} \alpha_{A} \Delta T = l_{B} \alpha_{B} \Delta T$$l_{A} \alpha_{A} = l_{B} \alpha_{B}$Substituting the given values:$l_{A} (18 	imes 10^{-6}) = l_{B} (27 	imes 10^{-6})$$l_{A} (18) = l_{B} (27)$$l_{A} = \frac{27}{18} l_{B} = 1.5 l_{B}$We know $l_{A} - l_{B} = 60 	ext{ cm}$.Substituting $l_{A} = 1.5 l_{B}$:$1.5 l_{B} - l_{B} = 60 	ext{ cm}$$0.5 l_{B} = 60 	ext{ cm}$$l_{B} = 120 	ext{ cm}$Then,$l_{A} = 1.5 	imes 120 = 180 	ext{ cm}$.

The difference in length between two rods $A$ and $B$ is $60 \text{ cm}$ at all temperatures. If $\alpha_{A} = 18 \times 10^{-6} /^{\circ}\text{C}$ and $\alpha_{B} = 27 \times 10^{-6} /^{\circ}\text{C}$,the lengths of the two rods are:

Similar Questions

The scale on a steel metre stick is calibrated at $20^{\circ}C$. The error in the reading of $50 \, cm$ at $30^{\circ}C$ is: (take linear expansion coefficient of steel $\alpha = 1.0 \times 10^{-5} / ^{\circ}C$)

Two holes of unequal diameters $d_1$ and $d_2$ $(d_1 > d_2)$ are cut in a metal sheet. If the sheet is heated,what happens to the diameters?

The coefficients of linear expansion of brass and steel rods are $\alpha_1$ and $\alpha_2$ respectively. The lengths of the brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2 - l_1)$ is maintained the same at all temperatures,which one of the following relations is correct?

Two metal plates $P$ and $Q$ of the same material are arranged as shown in the figure. If both the plates are uniformly heated through the same range of temperature,then

Two rods are joined between fixed supports as shown in the figure. The condition for no change in the total length of the system with an increase in temperature is given by:
($\alpha_1, \alpha_2$ = linear expansion coefficients,$A_1, A_2$ = cross-sectional areas of rods,$Y_1, Y_2$ = Young's moduli)

Vedclass Test Series

Exam Paper Generator

Online Exam Module