A charged cork of mass m suspended by a light string is placed in uniform electric field filed of strength `E = (hati+hatj) xx 10^(5)NC^(-1)` as shown in the figure. If in equilibrium position tension in the string is `2mg//(1+sqrt3)` the angle `alpha` with the vertical can be

Options

A. `60^@`
B. `30^@`
C. `45^@`
D. `18^@`

Answer

A, B

Explanation

a.,b.
`E_(x)=E_(y)=10^(5)NC^(-1)`
`qE_(x)=T sin a`,
`qE_(y)=mg -T cos a`
Dividing `(E_(x))/(E_(y))=(Tsin a)/(mg-T cos a)`
or `mg-T cos a=T sin a`
or `mg=(2mg)/(1+sqrt(3))(cosa+sin a)`
or `ocs a+sin a=(sqrt(3)+1)/(2),rArra=30^(@)` or `60^(@)`