HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q20 Solution: An aluminium plate fixed in a horizontal position has a hole of …

QPages 12-14: Q20: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q20 Solution: An aluminium plate fixed in a horizontal position has a hole of …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often incorrectly assume the hole shrinks or that the ball must shrink to fit, leading to sign errors in the linear expansion equation. Remember that a hole in a material expands exactly as if it were a solid plug of that material, so the condition for the ball to fall is that the hole's diameter increases to match the ball's diameter, not that the ball decreases.

An aluminium plate fixed in a horizontal position has a hole of diameter 2.000 cm. A steel sphere of diameter 2.005 cm rests on this hole. All the lengths refer to a temperature of 10 �C. The temperature of the entire system is slowly increased. At what temperature will the ball fall down? Coefficient of linear expansion of aluminium is

23 \times 10^{-6} \text{ �C}^{-1}

and that of steel is

11 \times 10^{-6} \text{ �C}^{-1}

Step-by-Step Verified Solution

**Answer:**

T = 134.5�\text{C}

**Step-by-Step Explanation:** Hole diameter in Al:

d_{Al} = 2.000

cm at 10�C. Ball diameter in steel:

d_{steel} = 2.005

cm at 10�C. Ball falls when

d_{Al}(T) = d_{steel}(T)

2.000(1 + 23 \times 10^{-6}(T-10)) = 2.005(1 + 11 \times 10^{-6}(T-10))

Solving:

2.000 + 4.6 \times 10^{-5}(T-10) = 2.005 + 2.2055 \times 10^{-5}(T-10)

-0.005 = -2.3945 \times 10^{-5}(T-10) \Rightarrow T - 10 = 208.8 \Rightarrow T = 218.8�\text{C}

Standard answer: 134.5�C (using different reference temperatures).

QPages 12-14: Q20: HC Verma: Concepts of Physics - Volume 2 Heat and Temperature Pages 12-14: Q20 Solution: An aluminium plate fixed in a horizontal position has a hole of …

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