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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

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

A typical atom has a diameter of about $1.0 \times 10^{- 10} m$ .

(a) What is this in inches?

(b) Approximately how many atoms are along a 1.0 cm line, assuming they just touch?

Jim stands beside a river and wonders how wide it is. He spots a large rock on the bank directly across from him. He then walks 65 strides upstream and judges that the angle between him and the rock, which he can still see, is at $30^{o}$ downstream (See below figure). Jim measures his stride to be about 0.8 m long. Estimate the width of the river.

A standard baseball has a circumference of approximately 23 cm. If a baseball had the same mass pear unit volume (see Tables in section 1–5) as a neutron or a proton, about what would its mass be?

What is the percent uncertainty in the measurement $5.48 \pm 0.25 m$ ?

See all solutions

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