Question

The kinetic energy of a particle depends on the square of speed of the particle. If error in measurement of speed of $30\%$, the error in the measurement of kinetic energy will be

• A. $30\%$
• B. $60\%$
• C. $69\%$
• D. $15\%$

Answer 1

Answer: (C)

$69\%$

$\begin{array}{cc}\text{Given -}& \text{error in measurement of speed}=30\%\\ & \text{error in measurement of kinetic energy}=?\end{array}$

$\begin{array}{c}\text{we have}\to \\ KE=\frac{1}{2}\cdot m\cdot v^2\end{array}$

$\begin{array}{c}\text{Since there is significant error more than}4\%\\ \text{so we cannot use error analysis method -}\end{array}$

$\text{let}\mathrm{case}1\to k=\frac{1}{2}m{v}_0^2$

$\begin{array}{cc}\text{case}2\to k_f& =\frac{1}{2}m\cdot {\left(1.3v_0\right)}^2\\ & =\frac{1}{2}m{v}_0^2\cdot \left(1.69\right)\end{array}$

$\begin{array}{cc}\Rightarrow k_f& =k\cdot \left(1.69\right)\\ \Rightarrow k_f-k=\left(0.69\right)k& \\ \Rightarrow \frac{\Delta k}{k}=0.69=69\%& \\ \text{\% error in kinetic energy.}& \end{array}$