Question

If the error in the measurement of momentum of a particle is 1% then the error in the measurement of kinetic energy is​

Answer 1

Answer:

▪️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.

▪️Hence the answer is 200%

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