A small sphere of mass $m =\ 0.5\, kg$ carrying a positive charge $q = 110\ \mu C$ is connected with a light, flexible and inextensible string of length $r = 60 \ cm$ and whirled in a vertical circle. If a vertically upwards electric field of strength $E = 10^5 NC^{-1}$ exists in the space, The minimum velocity of sphere required at highest point so that it may just complete the circle........$m/s$ $(g = 10\, ms^{-2})$
Diffcult
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$\mathrm{Fg}=5 \mathrm{\,N}, \quad \mathrm{Fe}=11 \mathrm{\,N}$
The minimum possible velocity at lowest point can be $\sqrt{7.2} \mathrm{\,m} / \mathrm{s} .$ The corresponding velocity at the highest point will also be minimum
${\frac{1}{2} m v_{f}^{2}-\frac{1}{2} m v_{i}^{2}=-m g(2 r)+q E_{0}(2 r)} $
${v_{s}=6 \,m / s}$
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