1. Tardigrade
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  4. In Millikan's oil drop experiment, an oil drop of radius and charge Q is held in equilibrium between the plates of a charged parallel plate capacitor when the potential difference is V. To keep a drop of radius 2 r and charge 2 Q in equilibrium between the plates, the potential difference V prime required is

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Q. In Millikan's oil drop experiment, an oil drop of radius and charge $Q$ is held in equilibrium between the plates of a charged parallel plate capacitor when the potential difference is $V$. To keep a drop of radius $2 r$ and charge $2 Q$ in equilibrium between the plates, the potential difference $V^{\prime}$ required is

Dual Nature of Radiation and Matter

Solution:

At equilibrium, $Q \cdot E=m g=\left(\frac{4}{3} \pi r^{3}\right) \rho \cdot g$
$\frac{Q \cdot V}{d}=\left(\frac{4}{3} \pi r^{3}\right) \rho \cdot g \Rightarrow V=\left(\frac{4}{3} \pi r^{3}\right) \frac{\rho \cdot g \cdot d}{Q}$
If charge becomes $2 Q$ and radius becomes $2 r,$ then
$V=\left[\frac{4}{3} \pi(2 r)^{3}\right] \frac{\rho \cdot g \cdot d}{(2 Q)} \Rightarrow V=\left(\frac{2^{3}}{2}\right) V=4 V$