Momentum is the product of the mass and velocity of an object and is a vector quantity. It is denoted by 'p' and is given by the equation p = mv.

Kinetic energy is the energy possessed by an object due to its motion and is a scalar quantity. It is denoted by 'K' and is given by the equation K = 1/2mv².



When we measure the momentum of a particle, there is always some uncertainty associated with it. This uncertainty is due to the limitations of the measuring instruments and the method used to take the measurement. The error in measurement of momentum is given by Δp/p, where Δp is the uncertainty in momentum and p is the actual momentum of the particle.

If the error in measurement of momentum is 100%, it means that Δp/p = 1. This implies that the uncertainty in momentum is equal to the actual momentum of the particle.



The error in measurement of kinetic energy is given by ΔK/K, where ΔK is the uncertainty in kinetic energy and K is the actual kinetic energy of the particle.

To find the error in measurement of kinetic energy, we first need to find the relationship between the uncertainty in momentum and the uncertainty in kinetic energy. This can be done using the following equation:

ΔK/K = 2(Δp/p)

Substituting the value of Δp/p as 1, we get:

ΔK/K = 2

This implies that the error in measurement of kinetic energy is 200%. In other words, the uncertainty in measurement of kinetic energy is twice the actual value of kinetic energy.



In conclusion, if the error in measurement of momentum of a particle is 100%, then the error in the measurement of kinetic energy is 200%. This is because there is a direct relationship between the uncertainty in momentum and the uncertainty in kinetic energy.