Advertisements
Advertisements
प्रश्न
A dimensionless quantity
विकल्प
never has a unit,
always has a unit,
may have a unit,
does not exist.
उत्तर
may have a unit
Dimensionless quantities may have units.
APPEARS IN
संबंधित प्रश्न
“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
India has had a long and unbroken tradition of great scholarship — in mathematics, astronomy, linguistics, logic and ethics. Yet, in parallel with this, several superstitious and obscurantistic attitudes and practices flourished in our society and unfortunately continue even today — among many educated people too. How will you use your knowledge of science to develop strategies to counter these attitudes ?
“It is more important to have beauty in the equations of physics than to have them agree with experiments”. The great British physicist P. A. M. Dirac held this view. Criticize this statement. Look out for some equations and results in this book which strike you as beautiful.
Suggest a way to measure the thickness of a sheet of paper.
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
The dimensions ML−1 T−2 may correspond to
Find the dimensions of
(a) angular speed ω,
(b) angular acceleration α,
(c) torque τ and
(d) moment of interia I.
Some of the equations involving these quantities are \[\omega = \frac{\theta_2 - \theta_1}{t_2 - t_1}, \alpha = \frac{\omega_2 - \omega_1}{t_2 - t_1}, \tau = F . r \text{ and }I = m r^2\].
The symbols have standard meanings.
Test if the following equation is dimensionally correct:
\[v = \sqrt{\frac{P}{\rho}},\]
where v = velocity, ρ = density, P = pressure
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?
Let \[\vec{A} = 5 \vec{i} - 4 \vec{j} \text { and } \vec{B} = - 7 \cdot 5 \vec{i} + 6 \vec{j}\]. Do we have \[\vec{B} = k \vec{A}\] ? Can we say \[\frac{\vec{B}}{\vec{A}}\] = k ?
The magnitude of the vector product of two vectors \[\left| \vec{A} \right|\] and \[\left| \vec{B} \right|\] may be
(a) greater than AB
(b) equal to AB
(c) less than AB
(d) equal to zero.
A vector \[\vec{A}\] makes an angle of 20° and \[\vec{B}\] makes an angle of 110° with the X-axis. The magnitudes of these vectors are 3 m and 4 m respectively. Find the resultant.
Two vectors have magnitudes 2 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is (a) 1 unit, (b) 5 unit and (c) 7 unit.
Suppose \[\vec{a}\] is a vector of magnitude 4.5 units due north. What is the vector (a) \[3 \vec{a}\], (b) \[- 4 \vec{a}\] ?
The changes in a function y and the independent variable x are related as
\[\frac{dy}{dx} = x^2\] . Find y as a function of x.
Write the number of significant digits in (a) 1001, (b) 100.1, (c) 100.10, (d) 0.001001.
In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 s. If the speed of sound in water is 1460 ms-1. What is the distance of an enemy submarine?
High speed moving particles are studied under
