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Question Number 155033 by peter frank last updated on 24/Sep/21

Answered by peter frank last updated on 25/Sep/21

work done=γ×△A=γ×(A_2 −A_1 )  A_1 =4πR^2   =1.256×10^(−3)     A_2 =nπr^2       n=?  from the conservation of volume  (4/3)πR^3 =n(4/3)πr^3   n=(R^3 /r^3 ) =1000    A_2 =nπr^2 =((R^3 /r^3 ) )πr^2  =1.256×10^(−2)   W.D=γ_(H_2 0) ×(A_2 −A_1 )

$$\mathrm{work}\:\mathrm{done}=\gamma×\bigtriangleup\mathrm{A}=\gamma×\left(\mathrm{A}_{\mathrm{2}} −\mathrm{A}_{\mathrm{1}} \right) \\ $$$$\mathrm{A}_{\mathrm{1}} =\mathrm{4}\pi\mathrm{R}^{\mathrm{2}} \:\:=\mathrm{1}.\mathrm{256}×\mathrm{10}^{−\mathrm{3}} \\ $$$$\:\:\mathrm{A}_{\mathrm{2}} =\mathrm{n}\pi\mathrm{r}^{\mathrm{2}} \:\:\:\:\:\:\mathrm{n}=? \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{conservation}\:\mathrm{of}\:\mathrm{volume} \\ $$$$\frac{\mathrm{4}}{\mathrm{3}}\pi\mathrm{R}^{\mathrm{3}} =\mathrm{n}\frac{\mathrm{4}}{\mathrm{3}}\pi\mathrm{r}^{\mathrm{3}} \\ $$$$\mathrm{n}=\frac{\mathrm{R}^{\mathrm{3}} }{\mathrm{r}^{\mathrm{3}} }\:=\mathrm{1000}\:\: \\ $$$$\mathrm{A}_{\mathrm{2}} =\mathrm{n}\pi\mathrm{r}^{\mathrm{2}} =\left(\frac{\mathrm{R}^{\mathrm{3}} }{\mathrm{r}^{\mathrm{3}} }\:\right)\pi\mathrm{r}^{\mathrm{2}} \:=\mathrm{1}.\mathrm{256}×\mathrm{10}^{−\mathrm{2}} \\ $$$$\mathrm{W}.\mathrm{D}=\gamma_{\mathrm{H}_{\mathrm{2}} \mathrm{0}} ×\left(\mathrm{A}_{\mathrm{2}} −\mathrm{A}_{\mathrm{1}} \right) \\ $$

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