Question

(1) The percentage error in the measurement
of mass and speed are 2% and 3% respectively
The error in Kinetic energy obtained by
measurement mass and speed will be​

Answer 1

Given :  Percentage error in mass, m = 2 %

             Percentage error in speed, v = 3 %

 To find :  Percentage error in kinetic energy

Solution :  As we know that,

${\boxed{\sf{Kinetic \ energy, \ k = {\dfrac{1}{2}} mv^2}}}$

• Expanding it in the language of error -

$\longrightarrow\sf{ {\dfrac{\triangle k}{k}} = {\dfrac{\triangle m}{m}} + 2 {\dfrac{\triangle v}{v}} }$

• Multipyling the above expression by 100 to find percentage error.  

$\longrightarrow\sf{ {\dfrac{\triangle k}{k}} \times 100 = {\dfrac{\triangle m}{m}} \times 100 + 2 {\dfrac{\triangle v}{v}} \times 100 }$

$\longrightarrow\sf{ {\dfrac{\triangle k}{k}} \times 100 = 2 + 2(3)}$

$\longrightarrow\sf{ {\dfrac{\triangle k}{k}} \times 100 = 8}$

Hence, the percentage error in kinetic energy is 8 %.