A huge capacitor of capacitance is charged to a huge voltage $\mathrm{V}$ and then discharged through a dc motor. The motor raises a mass $m$ through h comparable to earth's radius R. The capacitor energy is fully converted to the gravitational potential energy. If $h=R / 2$, then $V$ is…

Question

A huge capacitor of capacitance is charged to a huge voltage $\mathrm{V}$ and then discharged through a dc motor. The motor raises a mass $m$ through h comparable to earth's radius R. The capacitor energy is fully converted to the gravitational potential energy. If $h=R / 2$, then $V$ is equal to

Aicharya · Accepted Answer

The capacitor energy is $\frac{1}{2} \mathrm{CV}^{2}$ and $\mathrm{GPE}$ is $\left(\frac{m g h}{1+\frac{h}{R}}\right)$ So, we have $\frac{m g h}{1+\frac{h}{R}}=\frac{1}{2} C V^{2}$ If $h=R / 2$, then $m g R / 3=\frac{1}{2} C V^{2}$. This implies that $v=\sqrt{\frac{2m g R}{3 C}}$ ,

A huge capacitor of capacitance is charged to a huge voltage \(\mathrm{V}\) and then discharged through a dc…

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