Question

Assertion :When percentage errors in the measurement of mass and velocity are $1$% and $2$% respectively, the percentage error in K.E. is $5$%. Reason: $\frac{\Delta E}{E}=\frac{\Delta m}{m}+\frac{2\Delta v}{v}$

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect but Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Both Assertion and Reason are true and Reason is the correct explanation of assertion.

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

Differenting both side

$\frac{\Delta E}{E}=\frac{\Delta m}{m}+\frac{2\Delta v}{v}$

$\frac{\Delta E}{E}=\frac{1}{100}+2\times \frac{2}{100}=\frac{5}{100}=5$%