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p=(alpha)/(beta) exp (-(alphaz)/(K(B))th...

`p=(alpha)/(beta) exp (-(alphaz)/(K_(B))theta)`
`theta rarr Temperature " " P rarr Pressure`
`K_(B) rarr "Boltzman constant " Z rarr "Distance" `
Dimension of `(alpha//beta)` is -

A

`M^(0)L^(0)T^(0)`

B

`M^(-1)L^(1)T^(2)`

C

`M^(0)L^(2)T^(0)`

D

`ML^(-1)T^(-2)`

Text Solution

Verified by Experts

The correct Answer is:
D
`[(alpha)/(beta)]=[P]=ML^(-1)T^(-2)`
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BANSAL-UNIT DIMENSION, VECTOR & BASIC MATHS-EXERCISE-1 [SINGLE CORRECT CHOICE TYPE]
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  2. In the S.I. system, the unit of energy is-

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  3. The dimensions of the ratio of angular momentum to linear momentum is

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  4. If "Force" =X/("density")+C is dimensionally correct, the dimension of...

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  5. The dimensional formula for angular momentum is

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  6. For 10^((at+3)), the dimension of a is -

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  7. The velocity of a moving particle depends upon time t as v = at+(b)/(t...

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  8. Which of the following pairs of physical quantites does not have same ...

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  9. If F=ax+bt^(2)+c where F is force, x is distance and t is time. Then w...

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  10. If force, time and velocity are treated as fundamental quantities the...

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  11. Which of the following physical quantities do not have the same dimens...

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  12. Out of the following pair, which one NOT have identical dimensions is

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  13. The frequency f of vibrations of a mass m suspended from a spring of s...

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  14. p=(alpha)/(beta) exp (-(alphaz)/(K(B))theta) theta rarr Temperature ...

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  15. In Vander Wall's equation (P +(a)/(V^2))(V - b) = RT What are the dime...

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  16. In a new system of units, unit of mass is 10 kg, unit of length is 10...

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  17. The distance covered by a particle in time t is given by x=a+bt+ct^2+d...

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  18. A wave is represented by - y=a sin (At-Bx+C) where A, B, C are con...

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  19. If x=k sin (k l t), where x is displacement and t is time then dimensi...

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  20. If E , M , J , and G , respectively , denote energy , mass , angular m...

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