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The time dependence of a physical quanti...

The time dependence of a physical quantity P is given by `P=P_(0) exp (-alpha t^(2))`, where `alpha` is a constant and t is time. The constant `alpha`

A

will be dimensionless

B

will have dimensions of `T^(–2)`

C

will have dimensions as that of P

D

will have dimensions equal to the dimension of P multiplied by `T^(–2)`

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The correct Answer is:
B
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MOTION-UNITS AND DIMENSIONS, BASIC MATHEMATICS -Exercise - 1 (Objective Problems) (SECTION - B : Dimension and use of dimensions )
  1. A pair of physical quantities having the same dimensional formula are

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  2. The product of energy and time is called action. Therefore dimensional...

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  3. Dimensions of pressure are same as that of

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  4. Name the physical quantites having dimensions [M^1 L^2 T^(-2)].

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  5. Which one of the following has the dimensions of ML^(–1)T^(–2) ?

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  6. If area (A) velocity (v) and density (rho) are base units, then the di...

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  7. If alpha=F/v^(2) sin beta t, find dimensions of alpha and beta. Here v...

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  8. Given that v is speed, r is the radius and g is the acceleration due t...

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  9. If E,M,J and G respectively denote energy , mass angular momentum ...

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  10. The velocity of a freely falling body changes as g^ph^qwhere g is acce...

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  11. If a and b are two physical quantities having different dimensions the...

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  12. Two physical quantities whose dimensions are not same, cannot be :

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  13. The velocity (V) of a particle (in cm/s) is given in terms of time (t)...

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  14. The time dependence of a physical quantity P is given by P=P(0) exp (-...

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  15. Force F is given in terms of time t and distance x by F = A sin Ct + B...

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  16. If force (F) is given by F = Pt^(-1) + alpha t, where t is time. The u...

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  17. When a wave transverses in a medium, the displacement of a particle lo...

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  18. When a wave transverses in a medium, the displacement of a particle lo...

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  19. If force, acceleration and time are taken as fundamental quantities, t...

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  20. In a book, the answer for a particular question is expressed as b=(ma)...

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