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
?T
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 ?T
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1 Answer
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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 Vo= 3

Coefficient linear expansion =
Coefficient of volume expansion =3
3 , dV= 4 R3 =increase in volume
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