Question

The maximum error in the measurement of mass and length is 4% and 3% respectively. The error in the measurement of density of a cube will be

• A. 9 %
• B. 15 %
• C. 13 %
• D. 6 %

Hint:

When calculating errors in derived quantities, remember that powers of the measured quantities multiply their errors. For example, the error in density involves the error in mass and the error in the cube of length.

Answer 1

The Correct Option is C

Step 1: Understanding the error propagation.
The formula for the density \( \rho \) of a cube is: \[ \rho = \frac{m}{L^3} \] where \( m \) is the mass and \( L \) is the length. The error in the density is related to the errors in mass and length. For any function \( f(x, y) = \frac{x}{y^3} \), the maximum error in \( f \) is: \[ \frac{\Delta f}{f} = \frac{\Delta x}{x} + 3 \cdot \frac{\Delta y}{y} \] Thus, the total error in the density is the sum of the relative errors in mass and length. The given errors are 4% for mass and 3% for length. Therefore, the error in density is: \[ \Delta \rho = 4% + 3 \times 3% = 4% + 9% = 13% \] Step 2: Conclusion.
Thus, the correct answer is (C) 13 %.