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calculate the energy spent on spraying a drop of mercury of 1 cm radius into 10^6 droplets all of same radius. surface tension of mercury is 0.035N/m

Respuesta :

Answer:

ANS : .Energy spent on spraying =[tex]4.3542*10^{-4}J[/tex]

Explanation:

Given:

  • Radius of mercury = 1cm initially ;
  • split into [tex]10^{6}[/tex] drops ;

Thus, volume is conserved.

i.e ,

[tex]\frac{4}{3} \pi R_{o}^{3} = 10^{6}*\frac{4}{3} \pi R_{n}^{3}\\R_{n}=\frac{R_{o}}{10^{2}} = \frac{1cm}{100} = 0.01 cm[/tex]

  • Energy of a droplet = [tex]T[/tex]Δ[tex]A[/tex]

Where ,

  • T is the surface tension
  • ΔA is the change in area

Initial energy [tex]E_{i} = T*A_{i}\\= 0.0035 * 4 *\pi *0.01^{2}\\=4.398*10^{-6}J[/tex]

Final energy [tex]E_{f}=10^{6}*T*A_{f}\\=10^{6}*0.0035*4*\pi *(0.0001)^2\\=4.39823*10^{-4}[/tex]

∴  .Energy spent on spraying = [tex]=E_{f}-E{i}\\=(439.823-4.39823)*10^{-6}\\=4.3542*10^{-4}J[/tex]

ANS : .Energy spent on spraying =[tex]4.3542*10^{-4}J[/tex]

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