A steel rod at 25^{circ} C is observed to be | vedclass

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

Question

(B) Let $L_s$ be the length of the steel rod at $25^{\circ} C$ as measured by the metal scale. The scale is calibrated at $0^{\circ} C$, so at $25^{\c

Vedclass · Accepted Answer

$1.0002$

Vedclass · Answer

(B) Let $L_s$ be the length of the steel rod at $25^{\circ} C$ as measured by the metal scale. The scale is calibrated at $0^{\circ} C$, so at $25^{\circ} C$, its length expands. The length of $1 \ m$ on the scale at $25^{\circ} C$ corresponds to an actual length $L_{actual} = 1(1 + \alpha_{	ext{metal}} \Delta T) = 1(1 + 20 	imes 10^{-6} 	imes 25) = 1 + 0.0005 = 1.0005 \ m$.Now, this is the actual length of the steel rod at $25^{\circ} C$. Let $L_0$ be the length of the steel rod at $0^{\circ} C$.Using the thermal expansion formula for the steel rod: $L_{actual} = L_0(1 + \alpha_{	ext{steel}} \Delta T)$.$1.0005 = L_0(1 + 12 	imes 10^{-6} 	imes 25)$.$1.0005 = L_0(1 + 0.0003) = L_0(1.0003)$.$L_0 = \frac{1.0005}{1.0003} \approx 1.0001999 \ m \approx 1.0002 \ m$.

Similar Questions

$A$ metal rod $2 \,m$ long increases in length by $1.6 \,mm$, when heated from $0^{\circ} C$ to $60^{\circ} C$. The coefficient of linear expansion of the metal rod is:

$A$ cuboid $ABCDEFGH$ is anisotropic with $\alpha_x = 1 \times 10^{-5} /^{\circ}C$,$\alpha_y = 2 \times 10^{-5} /^{\circ}C$,$\alpha_z = 3 \times 10^{-5} /^{\circ}C$. The coefficient of superficial expansion of the faces can be:

$A$ solid metal sphere has a spherical cavity inside it. If the sphere is heated,the volume of the cavity will.....

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.

$A$ circular disc with a hole is shown in the figure. On heating,if the outer diameter $d_1$ increases by $0.3\%$,then the inner diameter $d_2$ will

Vedclass Test Series

Exam Paper Generator

Online Exam Module