Correct Answer - Option 4 : 5 %
CONCEPT:
-
Percentage error is the difference between theoretical value and an experimental, divided by the theoretical value, multiplied by 100 to give a percent.
- To calculate percentage error in the expression A = xmyn / zp . We use formula
\(\frac{{\Delta A}}{A} × 100 = m\frac{{\Delta x}}{x}× 100 + n\frac{{\Delta y}}{y} × 100+ p\frac{{\Delta z}}{z}× 100\)
where \(\frac{{\Delta A}}{A} × 100\) is the percentage error in A and \(\frac{{\Delta x}}{x} × 100\) is the percentage error in x.
- The Kinetic Energy (E) of an object due to its linear speed is given by:
E = 1/2 (m × v2)
where m is the mass of a body and v is the speed.
CALCULATION:
Given in the question:
\(\frac{{\Delta m}}{m}× 100 = 1\%\)
\(\frac{{\Delta v}}{v}× 100 = 2\%\)
Now we have to find the error in E = 1/2 (m × v2)
\(\frac{{\Delta E}}{E} × 100 = \frac{{\Delta M}}{M}× 100 + 2\frac{{\Delta v}}{v} × 100\)
\(\frac{{\Delta E}}{E} × 100 =1 + 2\times 2=5 \%\)
∴ % error in the estimation of the kinetic energy of the body is = 5%
- So the correct answer will option 4.
