A disc having uniform surface charge density in upper part `+rho` and `-rho` in lower half placed on rough horizontal surface as shown in figure. A uniform electric field is set up as shown if mass of disc is M and its radius is R as well sufficient friction is present to prevent slipping. The acceleration of disc is

Options

A. `(8)/(9)(rhoR^(2)E_(0))/(M)`
B. `(9)/(8)(rhoR^(2)E_(0))/(M)`
C. `(4)/(3)(rhoR^(2)E_(0))/(M)`
D. `(3)/(4)(rhoR^(2)E_(0))/(M)`

Answer

A

Explanation

Dipole moment `((sigmapiR^(2))/(2)) (2.(4R)/(3pi))`

`(4R^(3)sigma)/(3)`
`f_(r ) = Ma`
`(4R^(3)sigma)/(3)E - f_(r )R = (MR^(2))/(2)alpha`
`alpha = (a)/(R )`
For pure rolling
`a=(8)/(9)(rhoER^(2))/(M)`