An aluminium and steel rod having same length | vedclass

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

Question

(B) Given: Total length $L = 120 \ cm$ at $30^{\circ} C$. Since they have the same length, $\ell_0 = 60 \ cm$ for each rod.Change in temperature $\Del

Vedclass · Accepted Answer

$120.15$

Vedclass · Answer

(B) Given: Total length $L = 120 \ cm$ at $30^{\circ} C$. Since they have the same length, $\ell_0 = 60 \ cm$ for each rod.Change in temperature $\Delta T = 100^{\circ} C - 30^{\circ} C = 70^{\circ} C$.Coefficient of linear expansion for aluminium $\alpha_A = 24 	imes 10^{-6} /{ }^{\circ} C$.Coefficient of linear expansion for steel $\alpha_S = 1.2 	imes 10^{-5} /{ }^{\circ} C = 12 	imes 10^{-6} /{ }^{\circ} C$.The final length of the composite rod is the sum of the final lengths of the individual rods:$\ell_{	ext{final}} = \ell_0(1 + \alpha_A \Delta T) + \ell_0(1 + \alpha_S \Delta T)$$\ell_{	ext{final}} = \ell_0 [2 + (\alpha_A + \alpha_S) \Delta T]$$\ell_{	ext{final}} = 60 [2 + (24 	imes 10^{-6} + 12 	imes 10^{-6}) 	imes 70]$$\ell_{	ext{final}} = 60 [2 + (36 	imes 10^{-6}) 	imes 70]$$\ell_{	ext{final}} = 60 [2 + 0.00252] = 120 + 0.1512 = 120.1512 \ cm$.Rounding to two decimal places, the length is $120.15 \ cm$.

Similar Questions

If the volume of a block of metal changes by $0.12\%$ when it is heated through $20\,^{\circ}C$,the coefficient of linear expansion (in $^{\circ}C^{-1}$) of the metal is

On heating a uniform metallic cylinder, its length increases by $3 \%$. The area of cross-section of its base will increase by ........... $\%$

The length of a metallic rod is $5 \, m$ at $0^{\circ}C$ and becomes $5.01 \, m$ on heating up to $100^{\circ}C$. The coefficient of linear expansion of the metal is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module