What must be the lengths of steel and copper | vedclass

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

Question

(A) Let $L_S$ and $L_C$ be the lengths of steel and copper rods at $0^o C$.At any temperature $T$,the lengths are $L_S(1 + \alpha_S T)$ and $L_C(1 + \

Vedclass · Accepted Answer

$30\, cm$ for steel and $20\,cm$ for copper

Vedclass · Answer

(A) Let $L_S$ and $L_C$ be the lengths of steel and copper rods at $0^o C$.At any temperature $T$,the lengths are $L_S(1 + \alpha_S T)$ and $L_C(1 + \alpha_C T)$.The difference in lengths is given as $10\,cm$ at any temperature $T$,so:$L_S(1 + \alpha_S T) - L_C(1 + \alpha_C T) = 10$$(L_S - L_C) + (L_S \alpha_S - L_C \alpha_C)T = 10$For this to be independent of $T$,the coefficient of $T$ must be zero:$L_S \alpha_S - L_C \alpha_C = 0 \Rightarrow L_S \alpha_S = L_C \alpha_C$$L_S (1.2 	imes 10^{-5}) = L_C (1.8 	imes 10^{-5})$$L_S / L_C = 1.8 / 1.2 = 3 / 2$Also,from the first equation,$L_S - L_C = 10$.Substituting $L_S = 1.5 L_C$ into $L_S - L_C = 10$:$1.5 L_C - L_C = 10 \Rightarrow 0.5 L_C = 10 \Rightarrow L_C = 20\,cm$.Then $L_S = 1.5 	imes 20 = 30\,cm$.

What must be the lengths of steel and copper rods at $0^o C$ for the difference in their lengths to be $10\,cm$ at any common temperature? $(\alpha_{steel}=1.2 \times 10^{-5} \;^o C^{-1})$ and $(\alpha_{copper} = 1.8 \times 10^{-5} \;^o C^{-1})$

Similar Questions

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

The side of a copper cube is $1 \ m$ at $0^{\circ} C$. What will be the change in its volume,when it is heated to $100^{\circ} C$? $[\alpha_{\text{copper}} = 18 \times 10^{-6} /^{\circ} C]$

An aluminium sphere of $20 \; cm$ diameter is heated from $0^{\circ} C$ to $100^{\circ} C$. Its volume changes by (given that coefficient of linear expansion for aluminium $\alpha_{Al} = 23 \times 10^{-6} \; /^{\circ} C$): (in $; cm^3$)

$A$ solid ball of metal has a concentric spherical cavity within it. If the ball is heated,the volume of the cavity will

$A$ steel tape is calibrated at $20^{\circ} C$. On a cold day when the temperature is $-15^{\circ} C$,the percentage error in the tape will be ........... $\%$ $\left[\alpha_{\text{steel}} = 1.2 \times 10^{-5} {}^{\circ} C^{-1}\right]$

Vedclass Test Series

Exam Paper Generator

Online Exam Module