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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.
“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.
\[\int\frac{dx}{\sqrt{2ax - x^2}} = a^n \sin^{- 1} \left[ \frac{x}{a} - 1 \right]\]
The value of n is
Choose the correct statements(s):
(a) All quantities may be represented dimensionally in terms of the base quantities.
(b) A base quantity cannot be represented dimensionally in terms of the rest of the base quantities.
(c) The dimensions of a base quantity in other base quantities is always zero.
(d) The dimension of a derived quantity is never zero in any base quantity.
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.
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.
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 a vector have zero component along a line and still have nonzero magnitude?
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 \[\vec{A}\].
If \[\vec{A} \times \vec{B} = 0\] can you say that
(a) \[\vec{A} = \vec{B} ,\]
(b) \[\vec{A} \neq \vec{B}\] ?
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
The x-component of the resultant of several vectors
(a) is equal to the sum of the x-components of the vectors of the vectors
(b) may be smaller than the sum of the magnitudes of the vectors
(c) may be greater than the sum of the magnitudes of the vectors
(d) may be equal to the sum of the magnitudes of the vectors.
Add vectors \[\vec{A} , \vec{B} \text { and } \vec{C}\] each having magnitude of 100 unit and inclined to the X-axis at angles 45°, 135° and 315° respectively.
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 \[\overrightarrow{OA}, \overrightarrow{BC} \text { and } \overrightarrow{DE}\].
A carrom board (4 ft × 4 ft square) has the queen at the centre. The queen, hit by the striker moves to the from edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen (a) from the centre to the front edge, (b) from the front edge to the hole and (c) from the centre to the hole.
Suppose \[\vec{a}\] is a vector of magnitude 4.5 units due north. What is the vector (a) \[3 \vec{a}\], (b) \[- 4 \vec{a}\] ?
Let \[\vec{a} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j} + 5 \vec{k}\] Find the angle between them.
A curve is represented by y = sin x. If x is changed from \[\frac{\pi}{3}\text{ to }\frac{\pi}{3} + \frac{\pi}{100}\] , find approximately the change in y.
High speed moving particles are studied under
