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Concepts Of Physics MCQ Edition [Volume 2]PhysicsElectric Field and Potential

A ball having a mass of 100 g and a charge of 4.9 10⁻⁵ C is released from rest into an area containing a horizontal electric field of 2.0 10^4 N C ⁻¹ . Determine the resultant force acting on the ball.

Options

  1. A0.98 N making an angle of 45^ with the horizontal
  2. B1.4 N making an angle of 45^ with the horizontal
  3. C2.0 N making an angle of 45^ with the horizontal
  4. D1.4 N making an angle of 30^ with the horizontal

Correct answer

B. 1.4 N making an angle of 45^ with the horizontal

Step-by-step solution

Mass of the ball, m = 100 g = 0.1 kg Charge on the ball, q = 4.9 10⁻⁵ C Electric field, E = 2.0 10^4 N C ⁻¹ The gravitational force acting on the ball is vertically downwards: F_g = mg = 0.1 9.8 = 0.98 N The electric force acting on the ball is horizontal: F_e = qE = 4.9 10⁻⁵ 2.0 10^4 = 0.98 N Since F_g and F_e are perpendicular to each other, the magnitude of the resultant force is: F = F_g^2 + F_e^2 = (0.98)^2 + (0.98)^2 = 0.98 2 1.386 N 1.4 N The angle made by the resultant force with the horizontal is given by:

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