Advertisements
Advertisements
प्रश्न
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
विकल्प
can always be dimensionally represented in terms of L, T and x,
can never be dimensionally represented in terms of L, T and x,
may be represented in terms of L, T and x if a = 0,
may be represented in terms of L, T and x if a ≠ 0
उत्तर
may be represented in terms of L, T and x if a ≠ 0
If a = 0, then we cannot represent mass dimensionally in terms of L, T and x, otherwise it can be represented in terms of L, T and x.
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
“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?
Suggest a way to measure the thickness of a sheet of paper.
A physical quantity is measured and the result is expressed as nu where u is the unit used and n is the numerical value. If the result is expressed in various units then
A unitless quantity
\[\int\frac{dx}{\sqrt{2ax - x^2}} = a^n \sin^{- 1} \left[ \frac{x}{a} - 1 \right]\]
The value of n is
Find the dimensions of linear momentum .
Find the dimensions of magnetic field B.
The relevant equation are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]
where F is force, q is charge, v is speed, I is current, and a is distance.
Find the dimensions of magnetic permeability \[\mu_0\]
The relevant equation are \[F = qE, F = qvB, \text{ and }B = \frac{\mu_0 I}{2 \pi a};\]
where F is force, q is charge, v is speed, I is current, and a is distance.
Find the dimensions of the coefficient of linear expansion α and
Is a vector necessarily changed if it is rotated through an angle?
Let ε1 and ε2 be the angles made by \[\vec{A}\] and -\[\vec{A}\] with the positive X-axis. Show that tan ε1 = tan ε2. Thus, giving tan ε does not uniquely determine the direction of \[\vec{A}\].
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.
Refer to figure (2 − E1). Find (a) the magnitude, (b) x and y component and (c) the angle with the X-axis of the resultant of \[\overrightarrow{OA}, \overrightarrow{BC} \text { and } \overrightarrow{DE}\].
Prove that \[\vec{A} . \left( \vec{A} \times \vec{B} \right) = 0\].
If \[\vec{A} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{B} = 4 \vec{i} + 3 \vec{j} + 2 \vec{k}\] find \[\vec{A} \times \vec{B}\].
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.
