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Two physical quantities whose dimensions...

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

A

multiplied with each other

B

divided

C

added or substracted in the same expression

D

added together

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The correct Answer is:
To solve the question, we need to analyze the operations that can be performed on two physical quantities with different dimensions. ### Step-by-Step Solution: 1. **Understanding Physical Quantities**: - Physical quantities can have different dimensions. For example, velocity has the dimension of length (L) over time (T), while time has the dimension of time (T). 2. **Operations on Physical Quantities**: - **Multiplication**: Two physical quantities can be multiplied regardless of their dimensions. For example, if we multiply velocity (L/T) by time (T), we get displacement (L). - **Division**: Similar to multiplication, two quantities can be divided. For instance, dividing velocity (L/T) by time (T) gives us acceleration (L/T²). - **Addition/Subtraction**: This is where the dimensional analysis becomes critical. Two quantities can only be added or subtracted if they have the same dimensions. For example, you can add two lengths or two times, but you cannot add velocity (L/T) and time (T) because they have different dimensions. 3. **Conclusion**: - Therefore, the correct answer to the question is that two physical quantities whose dimensions are not the same cannot be added or subtracted in the same expression. ### Final Answer: Two physical quantities whose dimensions are not the same cannot be added or subtracted.
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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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