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प्रश्न
Choose the correct statements(s):
पर्याय
A dimensionally correct equation may be correct.
A dimensionally correct equation may be incorrect.
A dimensionally incorrect equation may be correct.
A dimensionally incorrect equation may be incorrect.
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उत्तर
A dimensionally correct equation may be correct.
A dimensionally correct equation may be incorrect.
A dimensionally incorrect equation may be incorrect.
It is not possible that a dimensionally incorrect equation is correct. All the other situations are possible.
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संबंधित प्रश्न
“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.
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What are the dimensions of the ratio of the volume of a cube of edge a to the volume of a sphere of radius a?
If two quantities have same dimensions, do they represent same physical content?
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The dimensions ML−1 T−2 may correspond to
Find the dimensions of magnetic permeability \[\mu_0\]
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where F is force, q is charge, v is speed, I is current, and a is distance.
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.
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 \[\vec{A}\].
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?
A situation may be described by using different sets coordinate axes having different orientation. Which the following do not depended on the orientation of the axis?
(a) the value of a scalar
(b) component of a vector
(c) a vector
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The magnitude of the vector product of two vectors \[\left| \vec{A} \right|\] and \[\left| \vec{B} \right|\] may be
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(b) equal to AB
(c) less than AB
(d) equal to zero.
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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.
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 \[\vec{A} \times \vec{B}\].
If \[\vec{A} , \vec{B} , \vec{C}\] are mutually perpendicular, show that \[\vec{C} \times \left( \vec{A} \times \vec{B} \right) = 0\] Is the converse true?
Write the number of significant digits in (a) 1001, (b) 100.1, (c) 100.10, (d) 0.001001.
