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प्रश्न
What are the dimensions of volume of a sphere of radius a?
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उत्तर
Volume of a sphere of radius a, V =` 4/3 pi ( a )^3`
i.e [ V ] = L × L × L = L3
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संबंधित प्रश्न
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 linear momentum .
Find the dimensions of frequency .
Find the dimensions of
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(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.
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(a) the specific heat capacity c,
(b) the coefficient of linear expansion α and
(c) the gas constant R.
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(b) \[\vec{A} \neq \vec{B}\] ?
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Let A1 A2 A3 A4 A5 A6 A1 be a regular hexagon. Write the x-components of the vectors represented by the six sides taken in order. Use the fact the resultant of these six vectors is zero, to prove that
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Use the known cosine values to verify the result.

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\[\frac{dy}{dx} = x^2\] . Find y as a function of x.
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