Question

Percentage error in kinetic energy of a body of mass $(60\pm 0.3)kg$ moving with velocity $(25\pm 0.1)m/s$ is

• A. $0.4\%$
• B. $0.2\%$
• C. $1.3\%$
• D. $3\%$

Answer 1

The correct option is C $1.3\%$

$\begin{array}{cc}\text{Given-}& \ast \text{Mass}M=60\pm 0.3kg\\ & \ast \text{velocity}v=25\pm 0.1m/8\end{array}$

$\begin{array}{c}\text{we know kinetic energy}k\\ k=\frac{1}{2}m\cdot v^2-\left(1\right)\end{array}$

$\begin{array}{c}\text{A By error analysis method -}\\ \text{- Taking logarithm both sides in eq-(1)}\\ \log \left(k\right)=\log \left(M\right)+2\cdot \log \left(v\right)+\log \left(\frac{1}{2}\right)\end{array}$

$\begin{array}{cc}& \frac{dk}{k}=\frac{dM}{M}+2\cdot \frac{dv}{v}\\ \Rightarrow & \frac{dk}{k}=\frac{0.3}{60}+\frac{0.1}{25}\times 2=1.3\%\end{array}$

$\text{Percentage error in kinetic energy is}1.3\%$