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  • The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is α.

The radius of a metal sphere at room temperature T is R, and the coefficient of linear expansion of the metal is \alpha. The sphere is heated a little by a temperature \Delta T so that its new Temperature is T+\Delta T. The increase in the volume of the sphere is approximately

(a) 2 \pi R \alpha \Delta T

(b) \pi R^{2} \alpha \Delta T

(c) \frac{ \pi R^{3} \alpha \Delta T}{3}

(d) 4 \pi R^{3} \alpha \Delta T

 

Answers (1)

The answer is the option 

Explanation: Here, we know that,

\alpha = coefficient of linear expansion

3\alpha= ϒ = coefficient of cubical expansion

Now, V_{0} = \frac{4}{3}\pi R^{3}

\gamma = \frac{\Delta V}{V\Delta T}

Thus, \Delta V=\gamma V\Delta T

i.e.,\Delta V=3\alpha .\frac{4}{3}\pi R ^{3}\Delta T

                    =4\pi R ^{3}\Delta T

Hence, opt (d).

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infoexpert24

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