A rod of length 20 , cm is made of metal A. I | vedclass

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

Question

(B) Let $l_1$ be the length of the portion of metal $A$ and $l_2$ be the length of the portion of metal $B$.Since the total length is $20 \, cm$,we ha

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(B) Let $l_1$ be the length of the portion of metal $A$ and $l_2$ be the length of the portion of metal $B$.Since the total length is $20 \, cm$,we have $l_1 + l_2 = 20 \, cm$.For a given change in temperature,the change in length $\Delta l$ is proportional to the initial length $l$. Thus,$\Delta l = \alpha \cdot l \cdot \Delta T$.For metal $A$,$\Delta l_A = 0.075 \, cm$ for $l = 20 \, cm$,so the expansion coefficient factor is $k_A = \frac{0.075}{20} = 0.00375$.For metal $B$,$\Delta l_B = 0.045 \, cm$ for $l = 20 \, cm$,so the expansion coefficient factor is $k_B = \frac{0.045}{20} = 0.00225$.The total expansion of the composite rod is $\Delta l_{total} = k_A l_1 + k_B l_2 = 0.06 \, cm$.Substituting $l_2 = 20 - l_1$:$0.00375 l_1 + 0.00225(20 - l_1) = 0.06$$0.00375 l_1 + 0.045 - 0.00225 l_1 = 0.06$$0.0015 l_1 = 0.015$$l_1 = \frac{0.015}{0.0015} = 10 \, cm$.

Similar Questions

The volume of a metal sphere increases by $0.24\%$ when its temperature is raised by $40^{\circ}C$. The coefficient of linear expansion of the metal is .......... $^{\circ}C^{-1}$.

On what value does the coefficient of linear expansion $\alpha_l$ depend? Write its unit.

$A$ uniform metal rod is used as a bar pendulum. If the room temperature rises by $10^{\circ}C$,and the coefficient of linear expansion of the metal of the rod is $2 \times 10^{-6} /^{\circ}C$,the period of the pendulum will have a percentage increase of:

$A$ steel tape of $300 \,cm$ length is graduated at $27^{\circ} C$. The length of a steel rod measured using the tape is found to be $110 \,cm$ at $50^{\circ} C$. The actual length of the steel rod at $50^{\circ} C$ is $(\alpha_{\text{steel}} = 1.2 \times 10^{-5} \,K^{-1})$. (in $\,cm$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module