# IMG-20190220-WA0002.jpgElectric charge of 10-3 C is uniformly distributed on a thin ring of radius 1 m. A particle of mass 0.9 g and carrying charge 1 micro columb is lying on the axis of the ring at a distance of 1 cm from centre. The angular frequency of the particle be (a) 100 rad/s (c) 5 rad/s (b) 10 rad/s (d) zero

Answers (1)
A Abhishek Sahu

Q-59

If we slightly displace the particle on the axis passing through the centre of the ring, the particle will perform SHM.

The net force on the particle will be, $F_{net} = \frac{-kQqx}{(R^{2}+x^{2})^{3/2}}$

As we know that $R>>x$

$\Rightarrow F_{net} = \frac{-kQqx}{R^{3}}$

$\Rightarrow F_{net} = -Kx$

$where \: K = \frac{-kQq}{R^{3}}$

$w = \sqrt{\frac{K}{m}}$

$\Rightarrow w = \sqrt{ \frac{-kQq}{mR^{3}}}$\Rightarrow w = \sqrt{ \frac{-kQq}{mR^{3}}}

$w = 100\: rad/s$

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