Question

If there is a positive error of $50\%$ in the measurement of velocity of a body, then the error in the measurement of kinetic energy is :

• A. $25\%$
• B. $50\%$
• C. $100\%$
• D. $125\%$

Answer 1

The correct option is C $100\%$

Given that,

$\frac{\Delta v}{v}\times 100$ is the % error in velocity = 50%

Kinetic energy $K.E=\frac{1}{2}m{v}^2$

Error in the kinetic energy

$\frac{\Delta K.E}{K.E}\times 100=m\times 2\frac{\Delta v}{v}\times 100$

$m$ is as a constant

Now, percentage error

$\frac{\Delta K.E}{K.E}\times 100=2\frac{\Delta v}{v}\times 100$

$\frac{\Delta K.E}{K.E}\times 100=2\times 50$%

$\frac{\Delta K.E}{K.E}\times 100=100$%

Hence, the error in the measurement of kinetic energy is $100$%