AP EAMCET · PHYSICS · Thermal Properties of Matter
An iron sphere having diameter \(D\) and mass \(M\) is immersed in hot water so that the temperature of the sphere increases by \(\delta T\). If \(\alpha\) is the coefficient of linear expansion of the iron then the change in the surface area of the sphere is
- A \(\pi D^2 \cdot \alpha \delta T(\alpha . \delta T-4)\)
- B \(\pi D^2 \cdot \alpha \cdot \delta T(\alpha \cdot \delta T+4)\)
- C \(\pi D^2 \cdot \alpha \cdot \delta T(\alpha . \delta T-2)\)
- D \(\pi D^2 \cdot \alpha . \delta T(\alpha . \delta T+2)\)
Answer & Solution
Correct Answer
(D) \(\pi D^2 \cdot \alpha . \delta T(\alpha . \delta T+2)\)
Step-by-step Solution
Detailed explanation
Given, diameter of sphere \(=D\) Initial surface area, \(A=4 \pi R^2\) \(=4 \pi\left(\frac{D}{2}\right)^2\) \(=\pi D^2\) ...(i) Surface area after heating by temperature \(\delta T\), \(A^{\prime}=4 \pi\left(\frac{D^{\prime}}{2}\right)^2=\pi\left(D^{\prime}\right)^2\) ...(ii)…
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