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Physics · PYQ NEET UG 2026

हिन्दी

The temperature of a metallic sphere of radius \( R \) is increased by a small amount \( \Delta T \). If the linear coefficient of thermal expansion of the metal is \( \alpha \), the approximate increase in the volume of the sphere is :

  1. A
    \( 2\pi R^3\alpha\Delta T \)
  2. B
    \( 3\pi R^3\alpha\Delta T \)
  3. C
    \( 4\pi R^3\alpha\Delta T \)
  4. D
    \( 6\pi R^3\alpha\Delta T \)
View Answer & Solution

Correct answer · Option C

\( 4\pi R^3\alpha\Delta T \)

Explanation

Volume \( V = \frac{4}{3}\pi R^3 \). Differentiating, \( \frac{\Delta V}{V} = 3\frac{\Delta R}{R} = 3\alpha\Delta T \). Thus \( \Delta V = 4\pi R^3 \alpha \Delta T \).
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