A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5}$ $mm$ at a certain temperature. The maximum temperature variation allowable during the ruling is .......... $^oC$ (Coefficient of linear expansion of steel $ = 10 \times {10^{ - 6}}{K^{ - 1}})$
A steel meter scale is to be ruled so that millimeter intervals are accurate within about $5 \times 10^{-5}$ $mm$ at a certain temperature. The maximum temperature variation allowable during the ruling is .......... $^oC$ (Coefficient of linear expansion of steel $ = 10 \times {10^{ - 6}}{K^{ - 1}})$
- A
$2$
- B
$5$
- C
$7$
- D
$10$
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Two metal strips that constitute a thermostat must necessarily differ in their
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- [IIT 1992]
A thin walled cylindrical metal vessel of linear coefficient of expansion $10^{-3} $ $^o C^{-1}$ contains benzenr of volume expansion coefficient $10^{-3}$ $^o C^{-1}$. If the vessel and its contents are now heated by $10^o C,$ the pressure due to the liquid at the bottom.
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A student records the initial length $l$, change in temperature $\Delta T$ and change in length $\Delta l$ of a rod as follows :
S.No.
$l(m)$
$\Delta T{(^o}C)$
$\Delta l(m)$
$(1)$
$2$
$10$
$4\times 10^{-4}$
$(2)$
$1$
$10$
$4\times 10^{-4}$
$(3)$
$2$
$20$
$2\times 10^{-4}$
$(4)$
$3$
$10$
$6\times 10^{-4}$
If the first observation is correct, what can you say about observations $2,\,3$ and $4$.
A student records the initial length $l$, change in temperature $\Delta T$ and change in length $\Delta l$ of a rod as follows :
| S.No. | $l(m)$ | $\Delta T{(^o}C)$ | $\Delta l(m)$ |
| $(1)$ | $2$ | $10$ | $4\times 10^{-4}$ |
| $(2)$ | $1$ | $10$ | $4\times 10^{-4}$ |
| $(3)$ | $2$ | $20$ | $2\times 10^{-4}$ |
| $(4)$ | $3$ | $10$ | $6\times 10^{-4}$ |
If the first observation is correct, what can you say about observations $2,\,3$ and $4$.
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A solid metallic cube having total surface area $24\;m ^{2}$ is uniformly heated. If its temperature is increased by $10\,^{\circ} C$, calculate the increase in volume of the cube $\left(\right.$ Given $\left.: \alpha=5.0 \times 10^{-4}{ }^{\circ} C ^{-1}\right)$
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Two rods of different materials having coefficient of linear expansion $\alpha_1$and $\alpha_2$ and Young's modulii $Y_1$ and $Y_2$ respectively are fixed between two rigid massive walls. The rods are heated such that they undergo the same increase in temperature. There is no bending of rods. If $\alpha_1:\alpha_2= 2 : 3$, the thermal stress developed in two rods are equal provided $Y_1 : Y_2$ is equal to
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