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Q.

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, {NCERT Exemplar]

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a

2πRα∆T

b

πR2α∆T

c

4πR3α∆T/3

d

4πR3α∆T

answer is D.

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Detailed Solution

Let the radius of the sphere be R. As the temperature increases, radius of the sphere increases as shown in figure.Original volume, Coefficient of linear expansion = α∴Coefficient of volume expansion = 3α∴  1VdVdT=3α⇒dV=3VαdT≈4πR3αΔT                    = Increase in the volume
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