Question

If error in the measurement of a momentum of a particle is 10% and mass is known exactly , the permissible error in the determination of kinetic energy is -------? GIVE A DETAILED ANSWER PLEASE....

Answer 1

Answer:

If the error in measurement of momentum of a particle is 10% and mass is known exactly, then what is the permissible error in? Short answer would be 21% error

Explanation:

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Answer 2

Answer:

Symbols used in this answer:-

Momentum=p

Velocity=v

Mass=m

Kinetic energy =KE

This question seems to be a usual error question but 10% is not a usual error . That’s a very big value to be measured incorrectly and as such the normal approach via differentiation will not be used here.

Momentum = mass * velocity_______(1)

Kinetic energy = 1/2 (mv^2)

i.e. Kinetic energy = 1/2m (mv)^2

i.e. Kinetic energy = 1/2m ( momentum)^2___(from1)

Now that we have KE= (p)^2 /2m____(2)

We have to find the error in the KE.

Now lets take the actual momentum (without error) as ‘x’

But their is 10% error in the measurement.

So, we may have two cases here------>

The measured value of p is x + (10% of x)

i.e. the measured momentum is 1.1x ______(3)

Put value of p from (3) into(2) we get :

KE =(1.1x)^2 /2m

i.e KE=1.21(x)^2/2m______(KE with error)_____(4)

But the true KE would be (x)^2/2m_____(5)