An inclinded plane making an angle of `30^(@)` with the horizontal electric field of `100 Vm^(-1)` as shown in Figure. A particle of mass `1 kg` and charge `0*01 C` is allowed to slide down from rest from a height of `1m`. If the coefficient of friction is 0*2, find time taken by the particle to reach the bottom.

Explanation

Here, ` theta = 30^(@), E = 100 Vm^(-1)`
`m = 1 kg, q = 0*01C`
`u = 0, h = 1 m, mu = 0*2`
`t = ?`
As is clear from Fig.
`R = mg cos 30^(@) + qE sin 30^(@)`
`= 1xx9*8 (sqrt(3))/(2) + 0*01xx100xx(1)/(2) = 8*9868`
Net force on the charged particale down the incline

`f = mg sin 30^(@) - qE cos 30^(@) - F (= muC)`
`= 1xx9*8xx(1)/(2) - 0*01xx100xx(sqrt(3))/(2) - 0*2xx8*9868`
`f = 4*9-0*866-1*7936 = 2*2404`
Acceleration of charged particle down the plane
`a = (f)/(m) = (2*2404)/(1) = 2*2404 m//s^(2)`
As `sin theta = (h)/(l), l = (h)/(sin theta) = (1)/(sin 30^(@)) = 2 m`
From `s = ut + (1)/(2) at^(2)`
`l = 0 + (1)/(2) xx 2*2404 t^(2)`
`t^(2) = (2l)/(2*2404) = (2xx2)/(2*2404) = 1*785`
`t = sqrt(1*785) = 1*336s`