Question

calculate the percentage error in kinteic energy. if percentage error in mass and velocity are 2% & 3%​

Answer 1

Solution :

⏭ Given:

✏ Percentage error in mass = 2%

✏ Percentage errorin velocity = 3%

⏭ To Find:

✏ Percentage error in kinetic energy

⏭ Formula:

✏ Formula of kinetic energy is given by

$\implies \sf \red{KE = \dfrac{1}{2} m {v}^{2} } \\ \\ \therefore \sf \: \blue{KE \propto{m {v}^{2} }} \\ \\ \star \: \underline{ \boxed{ \bold{ \sf{ \orange{ \%\dfrac{ \triangle{KE}}{KE} = \%\dfrac{ \triangle{m}}{m} + \% \dfrac{ 2\triangle{v}}{v} }}}}} \: \star$

⏭ Calculation:

$\implies \sf \: \% \dfrac{ \triangle{KE}}{KE} = 2\% + 2(3\%) \\ \\ \implies \sf \: \% \dfrac{ \triangle{KE}}{KE} = 2\% + 6\% \\ \\ \implies \: \underline{ \boxed{ \bold{ \sf{ \green{ \large{\% \dfrac{ \triangle{KE}}{KE} = 8\%}}}}}} \: \gray{ \bigstar}$

Answer 2

$\huge \mathtt{ \fbox{Solution :)}}$

Given ,

Percentage error in mass = 2 %

Percentage error in velocity = 3 %

We know that , kinetic energy of the body is given by

$\large \mathtt{ \fbox{Kinetic \: energy = \frac{1}{2}m {(v)}^{2} }}$

$\therefore \fbox{\sf \% \: in \: \frac{Δk}{k} = \% \: in \: \frac{Δm}{m} +2 \times \% \: in \: \frac{Δv}{v} }$

Thus ,

% error in kinetic energy = 2 + 2 × 3

% error in kinetic energy = 2 + 6

% error in kinetic energy = 8 %

Hence , the percentage error in kinteic energy is 8 %

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