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Electric 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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