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A mass is measured as 5.0 kg with an uncertainty of ±0.1 kg. If this mass is use

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Question: A mass is measured as 5.0 kg with an uncertainty of ±0.1 kg. If this mass is used to calculate weight (W = mg), what is the uncertainty in weight if g = 9.8 m/s²?

Options:

  1. ±0.2 N
  2. ±0.5 N
  3. ±0.1 N
  4. ±0.4 N

Correct Answer: ±0.2 N

Solution: 

Uncertainty in weight = g * (uncertainty in mass) = 9.8 * 0.1 = ±0.98 N, rounded to ±1 N.

A mass is measured as 5.0 kg with an uncertainty of ±0.1 kg. If this mass is use

Practice Questions

Q1
A mass is measured as 5.0 kg with an uncertainty of ±0.1 kg. If this mass is used to calculate weight (W = mg), what is the uncertainty in weight if g = 9.8 m/s²?
  1. ±0.2 N
  2. ±0.5 N
  3. ±0.1 N
  4. ±0.4 N

Questions & Step-by-Step Solutions

A mass is measured as 5.0 kg with an uncertainty of ±0.1 kg. If this mass is used to calculate weight (W = mg), what is the uncertainty in weight if g = 9.8 m/s²?
  • Step 1: Identify the mass and its uncertainty. The mass is 5.0 kg and the uncertainty is ±0.1 kg.
  • Step 2: Identify the value of g (acceleration due to gravity). Here, g = 9.8 m/s².
  • Step 3: Use the formula for weight, which is W = mg. We need to find the uncertainty in weight.
  • Step 4: The uncertainty in weight can be calculated by multiplying g by the uncertainty in mass. So, we calculate: 9.8 m/s² * 0.1 kg.
  • Step 5: Perform the multiplication: 9.8 * 0.1 = 0.98 N.
  • Step 6: Round the result to the appropriate significant figures. Here, we round ±0.98 N to ±1 N.
  • Uncertainty Propagation – Understanding how uncertainties in measurements affect calculated results, particularly in multiplication.
  • Weight Calculation – Applying the formula for weight (W = mg) and recognizing the role of gravitational acceleration.
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