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Chapter 1: Problem 14

The mass of a body of weight 200 gf is _____ \(\mathrm{g}\). (1) \(\quad 200\) (2) \(\quad 300\) (3) 400 (4) \(\quad 20\)

Short Answer

Expert verified
Answer: The mass of the body is 200,000 g.

Step by step solution

01

Write the given information

We are given the weight of the body, which is 200 gf.
02

Convert weight in gf to N using the conversion factor

1 gf is equivalent to the force exerted by 1g mass under Earth's gravity, which is equal to \(9.81 \, \mathrm{N/kg}\). To convert 200 gf to N, we can simply multiply it by the conversion factor: Weight (W) = 200 gf × \(9.81 \, \mathrm{N/kg}\) Weight (W) = 1962 \(\mathrm{N}\)
03

Calculate mass using the formula

We know that Weight (W) = Mass (m) × Acceleration due to gravity (g). So, Mass (m) = Weight (W) ÷ Acceleration due to gravity (g): Mass (m) = 1962 \(\mathrm{N}\) ÷ \(9.81 \, \mathrm{N/kg}\) Mass (m) = 200 \(\mathrm{kg}\)
04

Convert mass to grams

Since we want the mass in grams, we need to convert the mass from kg to g. We know that 1 kg = 1000 g. Mass (m) = 200 \(\mathrm{kg} \times 1000 \, \mathrm{g/kg}\) Mass (m) = 200,000 \(\mathrm{g}\) The correct answer is that the mass of the body is 200,000 g. This is not in the given options, so there might be an error in the problem or the options provided.

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