A blacksmith fixes an iron ring on the rim of | vedclass

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

Question

(B) Given:Initial temperature $T_{1} = 27^{\circ}C$Initial length (diameter) of the iron ring $L_{T1} = 5.231\; m$Final length (diameter) required $L_

Vedclass · Accepted Answer

$218$

Vedclass · Answer

(B) Given:Initial temperature $T_{1} = 27^{\circ}C$Initial length (diameter) of the iron ring $L_{T1} = 5.231\; m$Final length (diameter) required $L_{T2} = 5.243\; m$Coefficient of linear expansion $\alpha = 1.20 	imes 10^{-5} K^{-1}$Using the formula for linear expansion:$L_{T2} = L_{T1} [1 + \alpha(T_{2} - T_{1})]$Substituting the values:$5.243 = 5.231 [1 + 1.20 	imes 10^{-5} (T_{2} - 27)]$Divide by $5.231$:$1.002294 = 1 + 1.20 	imes 10^{-5} (T_{2} - 27)$$0.002294 = 1.20 	imes 10^{-5} (T_{2} - 27)$$T_{2} - 27 = \frac{0.002294}{1.20 	imes 10^{-5}}$$T_{2} - 27 \approx 191.17$$T_{2} \approx 191.17 + 27 = 218.17^{\circ}C$Rounding to the nearest integer,the temperature is $218^{\circ}C$.

Similar Questions

The ratio of linear expansivity to the coefficient of superficial expansion of a rectangular sheet of a solid is

Assertion :- $A$ brass disc is fast fitted in a hole in a steel plate. The system must be cooled to loosen the disc from the hole.
Reason :- The coefficient of linear expansion of brass is greater than the coefficient of linear expansion of steel.

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,then:

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 per $^{\circ}C^{-1}$) of the metal is :-

The length of a steel rod is $5 \ cm$ longer than a copper rod at all temperatures. What are the lengths of the steel and copper rods? (The coefficients of linear expansion for steel and copper are $1.1 \times 10^{-5} /{ }^{\circ} C$ and $1.7 \times 10^{-5} /{ }^{\circ} C$,respectively.)

Vedclass Test Series

Exam Paper Generator

Online Exam Module