A metal rod of length 20 , cm expands by 0.07 | vedclass

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

Question

(B) The formula for linear expansion is $\Delta L = L_0 \alpha \Delta 	heta$.For rod $A$: $0.075 = 20 	imes \alpha_A 	imes 100 \implies \alpha_A =

Vedclass · Accepted Answer

$10$

Vedclass · Answer

(B) The formula for linear expansion is $\Delta L = L_0 \alpha \Delta 	heta$.For rod $A$: $0.075 = 20 	imes \alpha_A 	imes 100 \implies \alpha_A = \frac{0.075}{2000} = 3.75 	imes 10^{-5} \, ^\circ C^{-1}$.For rod $B$: $0.045 = 20 	imes \alpha_B 	imes 100 \implies \alpha_B = \frac{0.045}{2000} = 2.25 	imes 10^{-5} \, ^\circ C^{-1}$.Let the length of metal $A$ be $x$ and the length of metal $B$ be $(20 - x)$.The total expansion of the composite rod is the sum of the expansions of its parts:$0.060 = (x \alpha_A \Delta 	heta) + ((20 - x) \alpha_B \Delta 	heta)$$0.060 = [x(3.75 	imes 10^{-5}) + (20 - x)(2.25 	imes 10^{-5})] 	imes 100$$0.060 = [3.75x + 45 - 2.25x] 	imes 10^{-3}$$60 = 1.5x + 45$$1.5x = 15$$x = 10 \, cm$.

Similar Questions

$A$ hole of diameter $5 \ cm$ is drilled in a metal sheet at $30^{\circ} C$. The coefficient of linear expansion of the metal is $2 \times 10^{-5} K^{-1}$. The diameter of the hole when the temperature is raised to $230^{\circ} C$ is equal to: (in $cm$)

The coefficient of volume expansion of a material is $5 \times 10^{-4} {^{\circ}C}^{-1}$. The fractional change in its density for a $40^{\circ}C$ rise in temperature is nearly.

What happens during the thermal expansion of a material when it is heated?

Solids expand on heating because ................

$A$ steel tape gives correct measurement at $20^{\circ} C$. $A$ piece of wood is being measured with the steel tape at $0^{\circ} C$. The reading is $25 \ cm$ on the tape. The real length of the given piece of wood must be:

Vedclass Test Series

Exam Paper Generator

Online Exam Module