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A block of mass 2 kg having a positive charge of 10 mC is projected with an initial velocity of 10 m s ⁻¹ on a rough horizontal surface. A uniform electric field of 400 N C ⁻¹ exists in the direction opposite to the initial velocity. If the coefficient of kinetic friction between the block and the surface is 0.3 , the distance travelled by the block before coming to rest is (Take g = 10 m s ⁻² )

Options

  1. A10 m
  2. B25 m
  3. C50 3 m
  4. D50 m

Correct answer

A. 10 m

Step-by-step solution

The block experiences two retarding forces: the electric force and the kinetic friction. Electric force, F_e = qE = 10 10⁻³ 400 = 4 N Frictional force, F_k = mg = 0.3 2 10 = 6 N Total retarding force, F_ net = F_e + F_k = 4 + 6 = 10 N Deceleration of the block, a = F_ net m = 10 2 = 5 m s ⁻² Using the third equation of motion, v^2 = u^2 - 2as 0 = (10)^2 - 2(5)s 10s = 100 s = 10 m Answer: 10 m

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