Question

solve the given problem​

Answer 1

Answer:

is question may achche say dekho then u can see that electric field is constant and the magnitude of electric field in both x and y direction is same .

now two vectors having same magnitude and makes 90 degree with each other implies that their resultant makes an angle 45 degree with the horizontal as well as vertical ....

now draw the free body diagram of the cork

forces acting on the cork are

in

+y axis direction the force acting is Tcos(alpha) + qEy

+x direction is qEx

-y direction is mg

-x direction is Tsin(alpha)

clearly we can see that Ex is Ecos45 and Ey is Esin45

now balancing the forces by equating them we get

Tcos(alpha) + qEsin45 = mg (balancing the vertical direction)...........(i)

Tsin(alpha) = qEcos45 ( balancing horizontal direction)..........(ii)

adding (i) and (ii) we get

Tcos(alpha) + Tsin(alpha) = qEcos45 + mg - qEsin45

implies

cos(Alpha) + sin(alpha) = mg/T

given that T = 2mg/(1+√3)

so we get

T = mg

------- × (1+√3)

2mg

implies

T = ( 1/2 + √3/2 )

now either alpha is equal to 30 degree or alpha is equal to 60 degree

if we put alpha is equal to 30 degree then we get

cos30degree + sin30degree = √3/2 + 1/2

also if we put alpha is equal to 60 degree then we get

cos60degree + sin60degree = 1/2 + √3/2

I hope it will help you