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


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