A body of capacity $4\mathrm{\mu }\mathrm{F}$ is charged to 80 V and another body of capacity $6\mathrm{\mu }\mathrm{F}$ is charged to 30V. When they are connected the energy lost by $4\mathrm{\mu }\mathrm{F}$ capacitor is 

Initial energy of body of capacitance $4\mathrm{\mu }\mathrm{F}$ is

${\mathrm{U}}_{\mathrm{i}}=\frac{1}{2}\times (4\times {10}^{-6}){\left(80\right)}^2=0.0128\mathrm{J}$

Final potential on this body after connection is 

$\mathrm{V}=\frac{4\times 80+6\times 30}{4+6}=50\mathrm{V}.$ So final energy on it 

${\mathrm{U}}_{\mathrm{f}}=\frac{1}{2}\times 4\times {10}^{-6}{\left(50\right)}^2=0.005\mathrm{J}$

Energy lost by this body $={\mathrm{U}}_{\mathrm{i}}-{\mathrm{U}}_{\mathrm{f}}=7.8\mathrm{mL}$