**Percentage Error in Velocity**

To calculate the percentage error in the measurement of kinetic energy, we need to first understand the concept of percentage error in velocity.

The percentage error in velocity is determined by comparing the difference between the measured value and the actual value of velocity, and then expressing this difference as a percentage of the actual value.

The formula to calculate percentage error is:

Percentage Error = (Measured Value - Actual Value) / Actual Value * 100

Let's assume the measured velocity of a particle is Vm and the actual velocity is Va. Using the formula, we can write:

Percentage Error in Velocity = (Vm - Va) / Va * 100

Given that the percentage error in velocity is 50%, we can substitute this value into the equation:

50 = (Vm - Va) / Va * 100

Simplifying the equation further, we get:

50 = Vm / Va * 100 - 100

Vm / Va * 100 = 150

Vm = 1.5 * Va

This means that the measured velocity is 1.5 times the actual velocity.

**Percentage Error in Kinetic Energy**

Now that we know the relationship between the measured and actual velocity, we can determine the percentage error in the measurement of kinetic energy.

The kinetic energy of a particle is given by the formula:

Kinetic Energy = (1/2) * m * V^2

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

Let's assume the measured kinetic energy is Km and the actual kinetic energy is Ka. Using the formula, we can write:

Percentage Error in Kinetic Energy = (Km - Ka) / Ka * 100

Now, we need to express the measured kinetic energy in terms of the actual kinetic energy using the relationship between measured and actual velocity.

Since kinetic energy depends on the square of velocity, we can write:

Km = (1/2) * m * (Vm^2)

Substituting the relationship Vm = 1.5 * Va, we get:

Km = (1/2) * m * (1.5 * Va)^2

Simplifying the equation further, we get:

Km = (1/2) * m * (2.25 * Va^2)

Km = 1.125 * m * Va^2

Now we can substitute this expression for Km into the percentage error formula:

Percentage Error in Kinetic Energy = (1.125 * m * Va^2 - Ka) / Ka * 100

This gives us the percentage error in the measurement of kinetic energy.

K.e =1/2mv^2 1/2 and mass are constant ∆ke/ke ×100= 2 ×∆v/v ×100 %error in k.e.... ∆k.e= 2×50 100%. ans