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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 $Δ T$ so that its new temperature is $(T + Δ T)$ . The increase in the volume of the sphere is approximately

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a

$2 π R α Δ T$

b

$π R^{2} α Δ T$

c

$4 π R^{3} α Δ T / 3$

d

$4 π R^{3} α Δ T$

answer is D.

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Detailed Solution

As $γ = \frac{Δ V}{V \times Δ T} a n d γ = 3 α$

$∴ 3 α = \frac{Δ V}{(\frac{4 π}{3} R^{3}) Δ T}$

Which gives , $Δ V = 4 π R^{3} α Δ T$

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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 sphere is heated a little by a temperature ΔTso that its new temperature is (T+ΔT). The increase in the volume of the sphere is approximately