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A small sphere of mass $m = 0.5 kg$ carrying a positive charge $q = 110 μ C$ is connected with a light, flexible and inextensible string of length $r = 60 c m$ and whirled in a vertical circle. If a vertically upward electric field of strength $E = 10^{5} N C^{- 1}$ exists in the space, calculate minimum velocity of sphere required at highest point so that it may just complete the circle. $(g = 10 {ms}^{- 2})$

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Detailed Solution

Upward force $q E > m g$ , So Tension in the string can’t be zero at the top most point, hence condition should be considered at lowest point
At lowest point $T - m g + q E = \frac{m V_{0}^{2}}{l}$ … (1)
$T = 0$
A using work energy theorem
$q E 2 l - m g 2 l = \frac{1}{2} m v^{2} - \frac{1}{2} m v_{0}^{2}$ … (2)
Solving (1) and (2) we get $V_{2} 6 m/s.$

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A small sphere of mass m=0.5 kg carrying a positive charge q=110μC is connected with a light, flexible and inextensible string of length r=60 cm and whirled in a vertical circle. If a vertically upward electric field of strength E=105NC−1 exists in the space, calculate minimum velocity of sphere required at highest point so that it may just complete the circle. (g=10 ms−2)