Advertisements
Advertisements
Question
The dimensions ML−1 T−2 may correspond to
Options
work done by a force
linear momentum
pressure.
energy per unit volume.
Advertisements
Solution
pressure
energy per unit volume
[Work done] = [ML2T−2]
[Linear momentum] = [MLT−1]
[Pressure] = [ML−1 T−2]
[Energy per unit volume] = [ML−1 T−2]
From the above, we can see that pressure and energy per unit volume have the same dimension, i.e., ML−1 T−2.
APPEARS IN
RELATED QUESTIONS
What are the dimensions of volume of a sphere of radius a?
If all the terms in an equation have same units, is it necessary that they have same dimensions? If all the terms in an equation have same dimensions, is it necessary that they have same units?
If two quantities have same dimensions, do they represent same physical content?
Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is, `[ x ] = M^a L^b T^c`. The quantity mass
Find the dimensions of frequency .
Find the dimensions of the coefficient of linear expansion α and
The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = \[13 \cdot 6\] , Density of \[\text{ water} = {10}^3 kg/ m^3 , g = 9 \cdot 8 m/ s^2\] at Calcutta. Pressure
= hpg in usual symbols.
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 it possible to add two vectors of unequal magnitudes and get zero? Is it possible to add three vectors of equal magnitudes and get zero?
Can you have \[\vec{A} \times \vec{B} = \vec{A} \cdot \vec{B}\] with A ≠ 0 and B ≠ 0 ? What if one of the two vectors is zero?
Which of the sets given below may represent the magnitudes of three vectors adding to zero?
The resultant of \[\vec{A} \text { and } \vec{B}\] makes an angle α with \[\vec{A}\] and β with \[\vec{B}\],
The component of a vector is
Prove that \[\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0\].
The electric current in a charging R−C circuit is given by i = i0 e−t/RC where i0, R and C are constant parameters of the circuit and t is time. Find the rate of change of current at (a) t = 0, (b) t = RC, (c) t = 10 RC.
Write the number of significant digits in (a) 1001, (b) 100.1, (c) 100.10, (d) 0.001001.
Round the following numbers to 2 significant digits.
(a) 3472, (b) 84.16. (c)2.55 and (d) 28.5
