A charged sphere of mass 2.8 kg is suspended from a string an electric force acts horizontally on the sphere so that the string makes angle 33 degree with vertical when at rest find magnitude of electric force and tension in string

Force, F = 17.82 N

T = 32.72 N

Explanation:

The mass of the sphere, m = 2.8 kg

Angle made by the string with the vertical, θ = 33°

The force, F, is said to act horizontally on the sphere, and the string makes angle 33° with the vertical. Check the free body diagram for the representation of the situation that is described.

Weight of the sphere, W = mg

W = 2.8 * 9.8

W = 27.44 N

Sin θ = F/T

sin 33 = F/T............(1)

cos θ = W/T

cos 33 = 27.44/T

T = 27.44/cos 33

T = 32.72 N

Put the value of T into equation (1)

sin 33 = F/32.72

F = 32.72 sin 33

F = 17.82 N

The magnitude of the Tension in the string = 32.72 N

The magnitude of the electric force on the ball = 17.82 N

Explanation:

The sketch of the free body diagram for the question is presented in the attached image to this solution.

Doing a force balance on the charged ball of sphere,

- T represents the tension in the string which acts away from the ball at angle 33° to the vertical. The tension can be split into a horizontal and a vertical component (Tₓ and Tᵧ respectively).

- Electric force, F, on the charged ball of sphere which acts horizontally to balance the the horizontal component of the tension in the string.

- The weight of the ball, W, which acts vertically downwards and balances the vertical component of the Tension.

Resolving the tension into the horizontal and vertical component

Tₓ = T sin 33° = (0.5446T) N

Tᵧ = T cos 33° = (0.8387T) N

W = mg = 2.8 × 9.8 = 27.44 N

(g = acceleration due to gravity = 9.8 m/s²)

Tᵧ = W

0.8387T = 27.44

T = (27.44/0.8387) = 32.72 N

F = Tₓ

F = 0.5446T = 0.5446 × 32.72 = 17.82 N

The magnitude of the Tension in the string = 32.72 N

The magnitude of the electric force on the ball = 17.82 N

Hope this Helps!!!

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