A point charge -Q is fixed at the centre of an insulated disc of mass M. The disc rests on a rough horizontal plane. Another charge having +Q is fixed vertically above the centre of the disc at a height of h. After the disc is displaced slightly in the horizontal direction (friction is sufficient to prevent slipping). If the period of oscillation of disc is found to be 2πhQnπε0Mh,
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Detailed Solution
Let the radius of the disc be R. If the disc is displaced 'x' the restoring torque τ about the point of contact of disc with groundτp=-(Fsin θ)R-(Fsinθ)R=Iα=MR22+MR2α ......(i)where F=Q24πε0h2+x2 ………(ii)and sin θ=xh2+x2 ……(iii)From (i), (ii) and (iii), we get-Q2xR4πε0h2+x23/2=MR22+MR2αor α=-Q2x6πε0MRh2+x23/2For x<