Question

Percentage error in the measurement of mass and speed are $2\%$ and $3\%$ respectively. The error in the estimation of kinetic energy obtained by measuring mass and speed will be

• A. $12\%$
• B. $10\%$
• C. $2\%$
• D. $8\%$

Answer 1

Answer: (D)

$8\%$

Answer 2

KInetic energy = $\frac{1}{2} mv^2$ Fractional error in kinetic energy $\frac{ \triangle K }{ K } = \frac{ \triangle m }{ m } + \frac{ 2 \triangle v }{ v }$ Percentage error in kinetic energy is $= \frac{ \triangle m }{ m } \times 100 + \frac{2 \triangle v }{ v } \times 100$ As we know, $\frac{ \triangle m }{ m } \times 2\%$ and $\frac{ \triangle v }{ v} \times 100 = 3\%$ So, percentage error in kinetic energy $= 2 + 2 \times 3 = 2 + 6$ $= 8\%$