Question

40. The percentage errors in the measurement of
mass and speed are 1% and 2% respectively.
What is the percentage error in the kinetic
energy
(A) 5%
(B) 2-5%
63%
(D) 1-5%.​

Answer 1

Answer:

The percentage error in the measurement of mass and speed are 1% and 2% respectively. What is the percentage error in kinetic energy?

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The nonrelativistic kinetic energy of a mass (m) moving at a speed, v, is , of course, given by:

K = m*v²/2

Here, both m and v have some uncertainty, and we want to know how that uncertainty propagates to the uncertainty in the kinetic energy.

Let's say x = a*uⁿ, and we know the fractional error in u. The rule for error propagation when raising to a power is:

σₓ/x = |n|*σᵤ/u

In this case, the fractional error in v² would then be:

σ_v²/v = 2*0.02 = 0.04

Now let x = a*u*v, where a is a constant and u and v have errors. If the errors are uncorrelated, they propagate as:

(σₓ/x)² = (σᵤ/u)² + (σᵥ/v)²

So in this case, the fractional error in the kinetic energy is given by:

σ_K/K = sqrt(0.01² + 0.04²) = sqrt(0.0017) ~= 0.0412, or 4.12%