Question

Que. Percenatge errors in the measurement of mass and speed are 2% and 3% respectively. The error in the estimate of kinetic energy obtained by measuring mass and speed will be?​

Answer 1

Answer:

Given:

Percentage error in Calculation of mass and speed is 2% and 3% respectively.

To find:

Error in estimating kinetic energy.

Concept :

Let mass be m and Velocity be v ,

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \boxed{ \sf{ke = \frac{1}{2} m {v}^{2}}}$

Now small error in mass and Velocity make small errors in Kinetic Energy, such that :

$\implies \sf{ \dfrac{ \Delta KE}{KE} = \dfrac{\Delta m}{m} + 2 \times \dfrac{\Delta v}{v}}$

Calculation:

Putting in all the values in the above equation :

$\implies \sf{ \dfrac{ \Delta KE}{KE} = 2\% + (2 \times 3\%)}$

$\implies \sf{ \dfrac{ \Delta KE}{KE} = 8\%}$

So final answer :

$\boxed{ \sf{ \large{ \red{max \: error = 8\%}}}}$

Additional information :

• Individual errors have to be added to get max error.
• This method can be applied on when the error is very small.
• Error % in individual quantities have to be less than 6%.

Answer 2

$\underline{ \boxed{ \bold{ \huge{ \purple{ \sf{Answer}}}}}} \\ \\ \star \sf \: \bold { Given} \\ \\ \mapsto \sf \: percentage \: error \: in \: mass = 2 \% \\ \\ \mapsto \sf \: percentage \: error \: in \: speed = 3\% \\ \\ \star \sf \: \bold {To \: Find} \\ \\ \mapsto \sf \: percentage \: error \: in \: kinetic \: energy \\ \\ \star \sf \: \bold{Formula} \\ \\ \mapsto \sf \: \boxed{ \bold{ \blue{KE = \frac{1}{2} m {v}^{2} }}} \\ \\ \mapsto \sf \: percentage \: error \: in \: KE \: is \: given \: as \\ \\ \mapsto \sf \boxed{ \bold{ \red{ \frac{ \Delta{KE}}{KE} = \frac{ \Delta{m}}{m} + 2 \frac{ \Delta{v}}{v} }}} \\ \\ \mapsto \sf \bold{Calculation} \\ \\ \mapsto \sf \: \% \frac{ \Delta{KE}}{KE} = 2\% + 2(3\%) = 8\% \\ \\ \therefore \: \underline{ \boxed{ \bold{ \green{ \sf{\% \frac{ \Delta{KE}}{KE} = 8\%}}}}}$