Chapter 1: Problem 13

If the density of a substance is \(2 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}\), then the mass of \(5 \mathrm{~m}^{3}\) of this substance is _______. (1) \(1000 \mathrm{~kg}\) (2) \(10000 \mathrm{~g}\) (3) \(10000 \mathrm{~kg}\) (4) Both (1) and (2)

Short Answer

Expert verified

Answer: (3) \(10000~kg\).

Step by step solution

Write down the given information

We are given: - Density of the substance, \(\rho = 2\times 10^3~kg/m^3\) - Volume of the substance, \(V = 5~m^3\) We need to find the mass of the substance.

Recall the formula for density

The formula for density is \(\rho = \frac{m}{V}\), where \(\rho\) is density, \(m\) is mass, and \(V\) is volume.

Rearrange the formula to solve for mass

We need to solve for mass, so we rearrange the density formula to isolate \(m\): \(m = \rho \times V\)

Plug in the given values

Substitute the given values for density and volume into the formula: \(m = (2\times 10^3~kg/m^3) \times (5~m^3)\)

Calculate the mass

Calculate the mass by multiplying the density and volume: \(m = 10^4~kg\) So, the mass of the substance is \(10000~kg\).

Match the answer with given options

The calculated mass matches with option (3) \(10000~kg\). Therefore, the correct answer is: (3) \(10000~kg\).

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If the density of a substance is \(2 \times 10^{3} \mathrm{~kg} \mathrm{~m}^{-3}\), then the mass of \(5 \mathrm{~m}^{3}\) of this substance is _______. (1) \(1000 \mathrm{~kg}\) (2) \(10000 \mathrm{~g}\) (3) \(10000 \mathrm{~kg}\) (4) Both (1) and (2)

Short Answer

Step by step solution

Write down the given information

Recall the formula for density

Rearrange the formula to solve for mass

Plug in the given values

Calculate the mass

Match the answer with given options

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