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If a substance is in the form of a long rod, for a small change in temperature $\Delta T$, the fractional change in length $\Delta l/l$ is directly proportional to $\Delta T$. The proportionality constant is known as:

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Explanation

The context states: 'If the substance is in the form of a long rod, then for small change in temperature, $\Delta T$, the fractional change in length, $\Delta l/l$, is directly proportional to $\Delta T$. where $\alpha_l$ is known as the coefficient of linear expansion (or linear expansivity)...'

The relationship between the coefficient of volume expansion ($\alpha_V$) and the coefficient of linear expansion ($\alpha_l$) for a material is:

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Explanation

The context explicitly states: 'The relation between them is : $\alpha_V = 3\alpha_l$'.

According to the provided table of coefficients of linear expansion, which material expands approximately five times more than glass (pyrex) for the same rise in temperature?

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Explanation

From Table 10.1, $\alpha_l$ for Glass (pyrex) is $0.32 \times 10^{-5} K^{-1}$ and for Copper is $1.7 \times 10^{-5} K^{-1}$. Comparing these, $1.7 / 0.32 \approx 5.3$, so copper expands about five times more than glass.

If a steel rod is prevented from expanding by fixing its ends rigidly while its temperature rises, the stress developed in the rod is called:

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Explanation

The context defines this phenomenon: 'What happens by preventing the thermal expansion of a rod by fixing its ends rigidly? Clearly, the rod acquires a compressive strain due to the external forces provided by the rigid support at the ends. The corresponding stress set up in the rod is called thermal stress.'

A balloon partially inflated in a cool room expands to full size when placed in warm water. This is an example of:

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Explanation

The context mentions: 'Similarly, in case of gases, a balloon partially inflated in a cool room may expand to full size when placed in warm water.' This describes the volume expansion of the air (a gas) inside the balloon.

The coefficient of linear expansion ($\alpha_l$) has units of:

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Explanation

The definition $\Delta l/l = \alpha_l \Delta T$ implies that $\alpha_l = (\Delta l/l) / \Delta T$. Since $\Delta l/l$ is dimensionless, the unit of $\alpha_l$ is the inverse of the unit of temperature change, which is $K^{-1}$ (or $^\circ C^{-1}$). The table also lists units as $10^{-5} K^{-1}$.

Which of the following materials typically has a higher value of coefficient of linear expansion?

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Explanation

The context states: 'Normally, metals expand more and have relatively high values of $\alpha_l$.' Table 10.1 confirms metals like Aluminium, Brass, Iron, Copper, Silver, Gold have higher values compared to Glass (pyrex) and Lead.

If a rectangular sheet of a solid material has a length 'a' and breadth 'b', and its temperature increases by $\Delta T$, the increase in length $\Delta a$ can be expressed as:

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Explanation

The example for area expansion shows that when the temperature increases by $\Delta T$, 'a' increases by $\Delta a = \alpha_l a \Delta T$ and 'b' increases by $\Delta b = \alpha_l b \Delta T$. This directly refers to linear expansion.

The phenomenon where a blacksmith heats an iron ring before fitting it on the rim of a wooden wheel of a horse cart is an application of:

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Explanation

The introduction section mentions: 'you will find out why blacksmiths heat the iron ring before fitting on the rim of a wooden wheel of a horse cart'. This is a classic application of thermal expansion, where the ring expands on heating, allowing it to fit, and then contracts on cooling, forming a tight fit.

Which of the following describes the inheritance pattern observed in the flower color of the dog flower (snapdragon)?

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Explanation

The text states: 'The inheritance of flower colour in the dog flower (snapdragon or Antirrhinum sp.) is a good example to understand incomplete dominance.' In incomplete dominance, the F1 phenotype is intermediate between the two parental phenotypes.

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