Advertisements
Advertisements
Question
What are the dimensions of volume of a sphere of radius a?
Advertisements
Solution
Volume of a sphere of radius a, V =` 4/3 pi ( a )^3`
i.e [ V ] = L × L × L = L3
APPEARS IN
RELATED QUESTIONS
Some of the most profound statements on the nature of science have come from Albert Einstein, one of the greatest scientists of all time. What do you think did Einstein mean when he said : “The most incomprehensible thing about the world is that it is comprehensible”?
“Every great physical theory starts as a heresy and ends as a dogma”. Give some examples from the history of science of the validity of this incisive remark
“Politics is the art of the possible”. Similarly, “Science is the art of the soluble”. Explain this beautiful aphorism on the nature and practice of science.
If two quantities have same dimensions, do they represent same physical content?
Find the dimensions of linear momentum .
Find the dimensions of pressure.
Find the dimensions of the coefficient of linear expansion α and
Let I = current through a conductor, R = its resistance and V = potential difference across its ends. According to Ohm's law, product of two of these quantities equals the third. Obtain Ohm's law from dimensional analysis. Dimensional formulae for R and V are \[{\text{ML}}^2 \text{I}^{- 2} \text{T}^{- 3}\] and \[{\text{ML}}^2 \text{T}^{- 3} \text{I}^{- 1}\] respectively.
Test if the following equation is dimensionally correct:
\[h = \frac{2S cos\theta}{\text{ prg }},\]
where h = height, S = surface tension, ρ = density, I = moment of interia.
Test if the following equation is dimensionally correct:
\[V = \frac{\pi P r^4 t}{8 \eta l}\]
where v = frequency, P = pressure, η = coefficient of viscosity.
Let x and a stand for distance. Is
\[\int\frac{dx}{\sqrt{a^2 - x^2}} = \frac{1}{a} \sin^{- 1} \frac{a}{x}\] dimensionally correct?
Is a vector necessarily changed if it is rotated through an angle?
Is the vector sum of the unit vectors \[\vec{i}\] and \[\vec{i}\] a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?
Let \[\vec{A} = 3 \vec{i} + 4 \vec{j}\]. Write a vector \[\vec{B}\] such that \[\vec{A} \neq \vec{B}\], but A = B.
Suppose \[\vec{a}\] is a vector of magnitude 4.5 units due north. What is the vector (a) \[3 \vec{a}\], (b) \[- 4 \vec{a}\] ?
Two vectors have magnitudes 2 m and 3m. The angle between them is 60°. Find (a) the scalar product of the two vectors, (b) the magnitude of their vector product.
Prove that \[\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0\].
Write the number of significant digits in (a) 1001, (b) 100.1, (c) 100.10, (d) 0.001001.
