P²=2mKE so error in measurement of momentum is 100 so error in measurement of the kinetic energy is 200
error in ke=2(error in momentum)

Error in the measurement of momentum:

The error in the measurement of momentum of a particle is given as (100). This value represents the uncertainty or deviation from the true value of the momentum. In physics, momentum is defined as the product of mass and velocity of an object. Mathematically, momentum (p) is given by the equation:

p = m * v

where m is the mass of the particle and v is its velocity.

Error in the measurement of kinetic energy:

To determine the error in the measurement of kinetic energy, we need to understand the relationship between kinetic energy and momentum. Kinetic energy (K) is given by the equation:

K = (1/2) * m * v^2

where m is the mass of the particle and v is its velocity.

Using the chain rule of differentiation, we can find the relationship between the errors in momentum and kinetic energy.

ΔK = (∂K/∂p) * Δp

where ΔK is the error in the measurement of kinetic energy and Δp is the error in the measurement of momentum.

Differentiating the equation for kinetic energy with respect to momentum (∂K/∂p), we get:

(∂K/∂p) = (∂K/∂m) * (∂m/∂p) + (∂K/∂v) * (∂v/∂p)

To simplify this expression, we can consider that the mass (m) of the particle is independent of its momentum (p) and the velocity (v) is directly proportional to momentum.

Therefore, (∂K/∂p) = (∂K/∂v) * (∂v/∂p)

Substituting this value back into the equation for the error in kinetic energy, we have:

ΔK = (∂K/∂p) * Δp
= (∂K/∂v) * (∂v/∂p) * Δp

Since velocity (v) is directly proportional to momentum (p), (∂v/∂p) can be written as 1/v. Thus, the equation becomes:

ΔK = (∂K/∂v) * (1/v) * Δp

Now, (∂K/∂v) represents the derivative of kinetic energy with respect to velocity, which is given by:

(∂K/∂v) = m * v

Substituting this value back into the equation for the error in kinetic energy, we get:

ΔK = (m * v) * (1/v) * Δp
= m * Δp

Therefore, the error in the measurement of kinetic energy (ΔK) is equal to the mass (m) of the particle multiplied by the error in the measurement of momentum (Δp). In this case, since the error in momentum is given as (100), the error in the measurement of kinetic energy would also be (100).