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Chapter 11: Q8MCQ (page 292)

\(\left( {{{\bf{L}}^{\bf{2}}}} \right)\)represents the dimensions for which of the following?

(a) cm2

(b) square feet

(c) m2

(d) All the above

Short Answer

Expert verified

The correct option is (d).

Step by step solution

01

Relation between the length and area

The dimension of any quantity is defined as the extent of the measurement of a particular kind. There are three fundamental dimensions with the help of which the others are derived.

You know that the dimension of the length is \(\left( {\rm{L}} \right)\). You also know that \({\rm{Area}} = {\left( {{\rm{Length}}} \right)^2}\).

02

Calculation of the dimension of the area

The dimension of the area is

\(\begin{aligned}{l}A = \left( {\rm{L}} \right)\left( {\rm{L}} \right)\\A = \left( {{{\rm{L}}^{\rm{2}}}} \right)\end{aligned}\).

Here, all the given options (cm2, square feet, and m2) represent the unit of the area.

Therefore, the answer will be that all the given options have the dimension \(\left( {{{\rm{L}}^{\rm{2}}}} \right)\).

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Most popular questions from this chapter

Carbon dioxide is a linear molecule. The carbon鈥搊xygen bonds in this molecule act very much like springs. Figure 11鈥�58 shows one possible way the oxygen atoms in this molecule can oscillate: the oxygen atoms oscillate symmetrically in and out, while the central carbon atom remains at rest. Hence each oxygen atom acts like a simple harmonic oscillator with a mass equal to the mass of an oxygen atom. It is observed that this oscillation occurs at a frequency \(f{\bf{ = 2}}{\bf{.83 \times 1}}{{\bf{0}}^{{\bf{13}}}}\;{\bf{Hz}}\). What is the spring constant of the C-O bond?

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