Question

An electric dipole of moment P is released in a uniform electric field E from the position of maximum torque. Angular speed of the dipole when P becomes parallel to E will be ( l= moment of inertia of dipole). ?
a) √2PE/l
b)√PE/I
c)√4PE/I
d)√2l/Pe
.
The answer is option. ( a ) Please explain how

Answer 1

refer to attachment mate

Answer 2

The correct answer to the question is option (a) √2PE/I

Given:

• An electric dipole P is released in a uniform electric field E from a position of maximum torque.
• I = Moment of inertia of dipole

To Find: Angular speed of the dipole when P is parallel to E.

Solution:

Torque of a given body = T = I α = - PEsin θ

where α is angular acceleration

α = - PE sin θ / I

ω [dω/dθ] =  - PE sin θ / I    (where ω = angular speed)

ω²/2 = - PE/I ∫ (0 → π/2) sin θ dθ

ω² =  - 2PE/I  (cos θ)  0 → π/2

ω² =  - 2PE/I ( - 1) = 2PE/I

ω = √2PE/I

The angular speed of the dipole when P is parallel to E = √2PE/I

#SPJ3