Question

The percentage error in the measurement of mass and speed are 2% and 3% respectively. How much will be the maximum error estimation of the kinetic energy obtained by measuring mass and speed?

Answer 1

Answer:

Maximum percentage error is 8%.

Given that the percentage error in the measurement of mass to as 2% and the speed to be as 3%

We have to find the maximum percentage error for the kinetic energy.

That is,  

Mass is denoted by m=2%,

Speed is denoted by v=3%

For kinetic energy we have $1 / 2 m v^{2}$

We have $\frac{\Delta m}{m}+2 \times \frac{\Delta v}{v}$

Now by substituting the values of m and v in the above expression,

= 2+2 x 3

= 2+6

=8

Hence maximum percentage error is to be 8%.

Answer 2

The maximum error estimation of the kinetic energy obtained by measuring mass and speed is 8%.

Given:

The percentage error in the measurement of mass and speed are 2% and 3%.

To Find:

The maximum error estimation of the kinetic energy is obtained by measuring mass and speed.

Solution:

Here, it is given that the mass and speed percentage are $2\%$ and $3\%$.

So, the kinetic energy of the particle is $KE=\frac{mv^{2} }{2}$.

now, the percentage error in the kinetic energy would be

$\frac{\triangle m}{m} \times100+2\frac{\triangle v}{v} \times 100$

here, after putting the given values in the above formula of the percentage error in the kinetic energy.

we get,

$=2+6$

now, by adding the mass and speed.

we get the maximum error estimation of the kinetic energy $=8\%$.

Hence, the maximum error estimation of the kinetic energy obtained by measuring mass and speed is 8%.

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