Question

If the error in the measurement of momentum of particle is 100% then the error in the measurement of kinetic energyif the error is a measurement of momentum of particle is + 100% then the error in the measurement of kinetic energy

Answer 1

Answer:

Explanation:

Kinetic energy = m*v*v/2 = p^2/2m

Here p = momentum = m*v

Now, let a slight change in a particular quantity 'X’ be dX

KE = p^2/(2m)

Taking logarithm on both sides,

log(KE) = 2log(p) - 2log(2m)

Differentiating on both sides,

d(KE)/KE = 2dp/p …(change in Mass is 0)

From this equation, we can observe that the error in measurement of Kinetic energy is twice that of momentum.