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Chapter 1: Q36. (page 19)

What are the dimensions of density, which is mass per volume?

Short Answer

Expert verified

The dimension of density is $M^{1} L^{- 3} T^{0}$ .

Step by step solution

01

Step 1. Pointing out the definition of density

You have already studied that density is the amount of mass per unit volume.

Given data:

$ρ = \frac{M}{V}$

where $ρ$ is the density, M is the mass, and V is the volume.

02

Step 2. Determining the dimensional formula for different quantities

You know that the unit of mass is kg, and the unit of volume is $m^{3}$ . Thus, the unit of density will be $kg \cdot m^{- 3}$ .

Similarly, the dimensional formula for mass is, localid="1654696905824" $[mass] = M^{1}$ .

The dimensional formula for volume is, localid="1654696917042" $[Volume] = L^{3}$ .

03

Step 3. Determining the dimensional formula of the density

The dimensional formula for density is:

$\begin{matrix} [Density] = \frac{[Mass]}{[Volume]} \\ = \frac{M^{1}}{L^{3}} \\ = M^{1} L^{- 3} T^{0} \end{matrix}$

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Most popular questions from this chapter

The speed vof an object is given by the equation $v = A t^{3} - B t$ , where trefers to time.

(a) What are the dimensions of A and B?

(b) What are the SI units for the constants Aand B?

What, approximately, is the percent uncertainty for a measurement given as $1.57 m^{2}$ ?

A storm dumps 1.0 cm of rain on a city that is 6 km wide and 8 km long in a 2 h period. How many metric tons (1 metric ton = $10^{3} kg$ ) of water fell on the city? ( $1 {cm}^{3}$ of water has a mass of $1 g = 10^{- 3} kg$ .) How many gallons of water was this?

A typical adult human lung contains about 300 million tiny cavities called alveoli. Estimate the average diameter of a single alveolus.

A certain compact disc (CD) contains 783.216 megabytes of digital information. Each byte consists of exactly 8 bits. When played, a CD player reads the CD’s information at a constant rate of 1.4 megabits per second. How many minutes does the player take to read the entire CD?

See all solutions

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