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Difficulty: MediumMeasurement of Mass and Weight

A body is weighed on a distant planet where the acceleration due to gravity is 4 m s−24\text{ m s}^{-2}. A spring balance calibrated on Earth (g=10 m s−2g = 10\text{ m s}^{-2}) gives a reading of 20 N20\text{ N} for the body on this planet. What is the mass of the body as measured by a beam balance on the planet?

  1. A
    2.0 kg2.0\text{ kg}
  2. 5.0 kg5.0\text{ kg}Answer
  3. C
    50.0 kg50.0\text{ kg}
  4. D
    80.0 kg80.0\text{ kg}

Answer

The mass of the body as measured by a beam balance is 5.0 kg5.0\text{ kg}.
The spring balance measures weight (W=mgplanetW = mg_{\text{planet}}). Substituting the given values (20 N=m×4 m s−220\text{ N} = m \times 4\text{ m s}^{-2}) gives m=5.0 kgm = 5.0\text{ kg}. Since mass is constant everywhere and a beam balance measures mass independently of local gravity variation, the beam balance reads 5.0 kg5.0\text{ kg}.

Step-by-Step Solution

1
Calculate the mass of the body using the spring balance reading on the planet.
m=Wplanetgplanet=20 N4 m s−2=5.0 kgm = \frac{W_{\text{planet}}}{g_{\text{planet}}} = \frac{20\text{ N}}{4\text{ m s}^{-2}} = 5.0\text{ kg}
Spring balances measure weight force (W=mgW = mg). The local weight divided by local gravity yields the mass.
2
Determine the reading on a beam balance.
The beam balance measures mass directly by comparison, yielding 5.0 kg5.0\text{ kg}.
Mass is an invariant property of matter and does not change with location or gravitational field strength.

Key Concept

Mass vs. Weight and Instrument Principles
Estimated Time:1m 0s
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Topics

Measurement of Mass and Weight

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