NEETPhysicsMathematics in Physics
The percentage errors in the measurement of mass, length, and time are 1 % , 2 % , and 3 % respectively. Match List-I (Physical Quantity) with List-II (Maximum Percentage Error) based on these measurements. List-I List-II (A) Velocity (I) 9 % (B) Acceleration (II) 11 % (C) Force (III) 5 % (D) Kinetic Energy (IV) 8 % Choose the correct answer from the options given below:
Options
- A(A)-(III), (B)-(IV), (C)-(I), (D)-(II)
- B(A)-(III), (B)-(IV), (C)-(II), (D)-(I)
- C(A)-(IV), (B)-(III), (C)-(I), (D)-(II)
- D(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
Correct answer
A. (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
Step-by-step solution
The maximum percentage error is calculated using the dimensional formula of each quantity, where errors are always added regardless of whether the power is positive or negative. For Velocity [LT⁻¹] : Maximum percentage error = %L + %T = 2 % + 3 % = 5 % . This matches (A) with (III). For Acceleration [LT⁻²] : Maximum percentage error = %L + 2( %T) = 2 % + 2(3 %) = 8 % . This matches (B) with (IV). For Force [MLT⁻²] : Maximum percentage error = %M + %L + 2( %T) = 1 % + 2 % + 2(3 %) = 9 % . This matches (C) with (I).