Question

The speed of a body is measured with a positive error of 30%. If the mass of the body is known exactly, the kinetic energy is calculated with an error of

• A. $60$%
• B. $30$%
• C. $69$%
• D. $39$%

Answer 1

Answer: (A)

$60$%

$\begin{array}{c}\text{Given: speed}=v\Rightarrow \frac{dv}{v}x\mid 0;\%=30\%\\ \text{mass}=m-\frac{dm}{m}\times 100\%=0\\ \text{kinetic energ}y=k=\frac{1}{2}m{v}^2\end{array}$

$\text{Taking log both side and differentiating}$

$\frac{\delta k}{k}=\frac{\delta m}{m}+2\frac{\delta v}{v}$

$\begin{array}{cc}\frac{\delta K}{K}\times 100& =\frac{\delta m}{m}\times 100\%+2\frac{\delta v}{v}\times 100\%\\ & =2\times 30\%\\ & =60\%\end{array}$