Question

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

Answer 1

Hint :

Error in kinetic energy is $$\frac{\Delta K}{K}$$

$$\textbf{Step1:Relation between kinetic energy and speed}$$

Kinetic Energy of particle is $$\frac{1}{2}mv^2$$

$$\Rightarrow$$$$K E \propto v^{2}$$

$$\Rightarrow$$$$\frac{\mathrm{KE}_{2}}{\mathrm{KE}_{1}}=\left(\frac{\mathrm{v}_{1}^{2}}{\mathrm{v}_{2}^{2}}\right)$$

$$\textbf{Step2:Relation between initial and final kinetic energies}$$

Given that the error in measure of speed is $$30 \%$$

$$\therefore \frac{\mathrm{KE}_{2}}{\mathrm{KE}_{1}}=\left(\frac{100+30}{100}\right)^{2}$$

$$\Rightarrow \frac{\mathrm{KE}_{2}}{\mathrm{KE}_{1}}=1.69$$

$$\Rightarrow \mathrm{KE}_{2}=1.69 \mathrm{KE}_{1}$$

$$\textbf{step3:Percentage change in kinetic energy}$$

Percentage change in kinetic energy is

$$=\frac{\mathrm{KE}_{2}-\mathrm{KE}_{1}}{\mathrm{KE}_{1}} \times 100$$

$$=\frac{1.69 \mathrm{KE}_{1}-\mathrm{KE}_{1}}{\mathrm{KE}_{1}}$$

$$=69 \%$$

Therefore the value of $$n \%$$ is $$69 \%$$.