Question

The bob of a simple pendulum has a mass of 2g and a charge of 5.0 µC. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is ______.

(take g = 10 m/s²)

Options

• tan^-1(2.0)

• tan^-1(0.2)

• tan^-1(5.0)

• tan^-1(0.5)

Answer 1

The bob of a simple pendulum has a mass of 2g and a charge of 5.0 µC. It is at rest in a uniform horizontal electric field of intensity 2000 V/m. At equilibrium, the angle that the pendulum makes with the vertical is tan^-1(0.5).

Explanation:

Given: A simple pendulum's bob mass

= 2g

= 2 × 10^-3 kg,

Charge on bob

= 5.0 µC

= 5.0 × 10^-6 C,

The applied electric field's intensity = 2000 V/m.

To find: The pendulum makes an angle with the vertical, θ.

Balancing the forces in the bob's equilibrium position:

T cosθ = mg; T sinθ = qE

That gives,

tanθ = `(qE)/(mg)`

`theta = tan^-1  ((qE)/(mg)) = (5.0 xx 10^-6 xx 2000)/(2 xx 10^-3 xx 10)`

= `tan^-1(0.5)`.