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JEE Main202310 Apr 2023Morning ShiftPhysicsMathematics in PhysicsActual

A physical quantity P is given as P = a 2 b 3 c d . The percentage error in the measurement of a , b , c and d are 1 % , 2 % , 3 % and 4 % respectively. The percentage error in the measurement of quantity P will be

Options

  1. A13 %
  2. B16 %
  3. C12 %
  4. D14 %

Correct answer

A. 13 %

Step-by-step solution

The given quantity is P = a 2 b 3 c d . The percentage error for a quantity can be given by the formula ∆ x x × 100 . Relation of the relative errors will be, Δ P P = 2 Δ a a + 3 Δ b b + Δ c c + 1 2 Δ d d Hence, the percentage error is calculated by substituting the values, Δ P P × 100 = 2 × 1 + 3 × 2 + 3 + 1 2 × 4 = 13 % .

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