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A cube is balanced on a beam balance and a spring balance. The reading on the beam balance is 6000 grams, and the reading on the spring balance is 60 N. However, the spring balance records 59.8 N. Explain this difference.

Answer :

The beam balance measures the mass (6000 grams or 6 kg directly), and the spring balance measures the force due to gravity acting on the mass (about 59.8 N). The slight discrepancy in the spring balance reading could be due to calibration errors or air buoyancy effects.

The difference between the readings on the beam balance and the spring balance with respect to the cubes can be explained through the differences in what each instrument measures and how they function.

Beam Balance: A beam balance measures mass. When you place an object on one side of a beam balance and balance it with standard weights on the other side, you are directly measuring the mass of the object. In this case, the beam balance gives a reading of 6000 grams, which is equivalent to 6 kilograms.

Spring Balance: A spring balance measures force, more specifically the normal force exerted by the object due to gravity. This is why the reading is given in Newtons (N). To find the weight (force due to gravity) using the mass of the object, you use the formula:

[tex]F = m \cdot g[/tex]

where

  • [tex]F[/tex] is the force in Newtons (N)
  • [tex]m[/tex] is the mass in kilograms (kg)
  • [tex]g[/tex] is the acceleration due to gravity ([tex]9.8 m/s^2[/tex])

For a mass of 6 kg:

[tex]F = 6 \text{ kg} \cdot 9.8 m/s}^2= 58.8 \text{ N}[/tex]

Explanation of Difference: The reading on the spring balance is slightly less, at 59.8 N compared to 60 N. This small difference can be due to several factors:

  • Calibration Error: Spring balances need to be properly calibrated, and even a small error in calibration can lead to a difference in readings.
  • Air Buoyancy: The presence of air can slightly buoy objects, causing a minute difference in weight measurement. This effect is more noticeable with highly sensitive instruments.

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