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A semi-circular ring of mass m and radius R with linear charge density $- λ,$ hinged at its centre with the help of a massless spoke as shown, is placed in a uniform electric field as shown in the figure. If the ring is slightly rotated about O in the plane of paper and released. Take $m = 8 k g, λ = 2 C / m$ and $E = 2 N / C .$ The time period of oscillation is $x π \sec$ .Find $x$ .

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Detailed Solution

$T = 2 π \sqrt{\frac{I}{m g . L_{C}}} P u t I = m R^{2} g = \frac{λ . E}{m}$

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