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Consider the following arrangement and c...

Consider the following arrangement and choose the correct options

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We know, dimensional formulae of `T, l and g ` are `[T], [L], [LT^(-2)]` respectively.
`:.` Dimensional formula of `sqrt(l/g) = sqrt(L/(LT^(-2))) = sqrt(T^2) = [T]`
Dimensional formula of left side is also [T]. As `2 pi` is a dimensionless quantity, the dimensional formula of left hand side of hte equation is equal to dimensional formula of right hand side. Hence we conclude that the given equation is correct one.
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AAKASH SERIES-UNITS AND MEASUREMENT-PRACTICE EXERCISE
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  3. If units in two systems of measurments are in the ratio 2 : 3, the rat...

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  4. If the unit of length is 4 m and that of velocity is 6 ms^(-1) , the u...

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  5. If the unit of force is 1N, the unit of work done is 10 J and the unit...

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  6. If the unit of length , mass and time each be doubled , the unit of wo...

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  7. A new unit of length is chosen such that the speed of light is vacuum ...

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  8. In planetary motion the areal velocity of position vector of a planet ...

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  9. If pressure P, velocity V and Time T are taken as fundamental physical...

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  10. The reverberation period T of a room on its volume V, its surface area...

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  11. If the vibration frequency of atoms in a crystaal depends on the atomi...

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  12. The time period of a soap bubble is T which depneds on pressure p dens...

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  13. The method of dimensional analysis can be used to derive which of the ...

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  14. If the velocity is represented by V, force by F and work by W . These ...

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  15. If C the velocity of light, h planck's constant and G Gravitational co...

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  16. If m is the mass of drop of a liquid of radius 'r' then (mg)/(pi r) ha...

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  17. The dimensionally correct formula is

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  18. The expression S = a/b (1 - e^(-bt)) is dimensionally true. The dimens...

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  19. According to Bernoullis theoram p/d + (v^2)/2 + gh = constant, dimensi...

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  20. If R is the electric resistance and C is the capacitance, the dimensio...

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  21. Velocity of sound in a medium is given by A^(1//2) d^(-1//2), where 'd...

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