Question

The percentage errors in the measurement of mass and speed are 3% and 4% respectively. The maximum error in the measurement of kinetic energy is.

• A. 11%
• B. 10%
• C. 8%
• D. 9%

Answer 1

The correct option is A 11%

$K.E=\frac{1}{2}m{v}^2$

$\Rightarrow log(K.E)=$ $log\left(\frac{1}{2}m{v}^2\right)$

On differentiating both sides, we get

$\frac{\Delta K.E}{K.E}=\frac{\Delta m}{m}$ $+\frac{2\Delta v}{v}$

$\frac{\Delta K.E}{K.E}=3+2\left(4\right)=11$

So, The maximum error in the measurement of kinetic energy is $11\%$.

Therefore, A is correct option.