The mass of a body Magar Dastan plus minus 0.2 gram and its velocity is measured as 2 + - 0.1 CM its Momentum will be

To find the momentum of a body, we use the formula for momentum, which is defined as the product of mass and velocity. The formula can be expressed as:

Momentum Calculation

Momentum (p) is calculated using the equation:

p = m × v

Where:

• p = momentum
• m = mass of the body
• v = velocity of the body

Given Values

From your question, we have:

• Mass (m) = 1 gram ± 0.2 grams
• Velocity (v) = 2 cm/s ± 0.1 cm/s

Calculating Momentum

First, let's calculate the nominal momentum using the central values of mass and velocity:

p = 1 g × 2 cm/s = 2 g·cm/s

Determining Uncertainty in Momentum

Next, we need to consider the uncertainties in both mass and velocity to find the uncertainty in momentum. The formula for the propagation of uncertainty in multiplication is:

Δp/p = Δm/m + Δv/v

Where:

• Δp = uncertainty in momentum
• Δm = uncertainty in mass
• Δv = uncertainty in velocity

Now, substituting the values:

• Δm = 0.2 g
• m = 1 g
• Δv = 0.1 cm/s
• v = 2 cm/s

Calculating the relative uncertainties:

Δp/p = (0.2/1) + (0.1/2)

Δp/p = 0.2 + 0.05 = 0.25

Finding Absolute Uncertainty in Momentum

Now, we can find the absolute uncertainty in momentum:

Δp = p × Δp/p

Δp = 2 g·cm/s × 0.25 = 0.5 g·cm/s

Final Result

Thus, the momentum of the body, including its uncertainty, is:

p = 2 g·cm/s ± 0.5 g·cm/s

This means that the momentum can vary between 1.5 g·cm/s and 2.5 g·cm/s, reflecting the uncertainties in both mass and velocity measurements. Understanding how to calculate momentum and its uncertainties is crucial in physics, as it helps in analyzing the motion of objects accurately.