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Chapter 1: Problem 54

54\. Ten identical metallic balls of density \(5 \mathrm{~g} \mathrm{~cm}^{-3}\) when dropped into water, the volume of the water displaced is found to be \(500 \mathrm{~cm}^{3}\). Determine the mass of each metallic ball.

Short Answer

Expert verified
Answer: The mass of each metallic ball is 250 g.

Step by step solution

01

Calculate the total mass of all the balls

To find the total mass, we will use the formula for density: Density = \(\frac{mass}{volume}\) We are given the density as \(5 \mathrm{~g} \mathrm{~cm}^{-3}\) and the total volume of water displaced as \(500 \mathrm{~cm}^{3}\). We can solve for the mass by rearranging the formula: Total mass = Density × Total volume
02

Calculate the total mass

Now, Multiply the density and total volume to find the total mass of all balls: Total mass = \(5 \mathrm{~g} \mathrm{~cm}^{-3} \times 500 \mathrm{~cm}^{3}\) = \(2500 \mathrm{~g}\)
03

Determine the mass of each ball

We are given that there are 10 identical metallic balls. So, we can find the mass of each ball by dividing the total mass by the number of balls: Mass of each ball = \(\frac{Total \:mass}{Number \:of \:balls}\) Mass of each ball = \(\frac{2500 \mathrm{~g}}{10}\) = \(250 \mathrm{~g}\) So, the mass of each metallic ball is \(250 \mathrm{~g}\).

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