A non conducting solid sphere of mass `m` and radius `R` having uniform charge density `+rho` and `-rho` as shown in figure. It is then placed on a rough non conducting horizontal plane. At `t=0` a uniform electric field `vecE=E_(0)hati N//C` is switched on and the solid sphere starts rolling with sliding. The magnitude of frictional force at `t=0` is `(2rhopiR^(3)E_(0))/K`. Find the value of `K`

Answer

7

Explanation

`tau_(Q)=PEsin53^(@)`
`=(rho2/3 pi R^(3))((3R)/4)E_(0) 4/5`
`=2/5 rhopiR^(4)E_(0)=(7/5 mR^(2) alpha)`
`a_(cm)=R alpha=2/7 (rhopiR^(3)E_(0))/m`
`f=ma_(cm)=2/7 rhopi R^(3)E_(0)`