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

(a) 2παR?T

(b) πR²α?T

(c) 4πR³?T/3

(d) 4παR³ $α$ ?T

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Payal Gupta | Contributor-Level 10

8 months ago

This is a multiple choice answer as classified in NCERT Exemplar

(d) Let radius of sphere be R . as the temperature increases radius of the sphere increases.

Original volume V_o= $\frac{4}{3} π R$ ³

Coefficient linear expansion = $α$

Coefficient of volume expansion =3 $α$

$\frac{d V}{V d T} =$ 3 $α$ , dV= 4 $π$ R³ $α ? T$ =increase in volume

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This is a multiple choice answer as classified in NCERT Exemplar

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