The percentage error in the measurement of the mass of a body is 1% and the percentage error in the measurement of velocity is 2%. Find the percentage error in the estimation of the kinetic energy of a body.

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.