Question

If the error in measurement of monentum of particle is $100\%$ then error in the measurement of kinetic energy

• A. $150$
• B. $100$
• C. $200$
• D. $300$
  

Answer 1

Answer: (D)

$300$

The relation between the kinetic energy and the momentum of a particle is:

$KE=\frac{p^2}{2m}$

let the actual momentum of the particle be $p$.

Since we know that the error in the measurement of momentum is 100%, the measurement of the momentum would come out to be $2p$.

So, the percentage error in the measurement of the kinetic energy can be obtained as:

$\%error=\frac{K{E}_f-K{E}_i}{K{E}_i}\times 100$

Here, $K{E}_i$ is the kinetic energy measured without error and $K{E}_f$ is the kinetic error with error in measurement.

$\%error=\frac{\frac{(2p{)}^2}{2m}-\frac{p^2}{2m}}{\frac{p^2}{2m}}\times 100$

$=3\times 100\%=300\%$

So, error in the measurement of Kinetic energy will be $300\%$.