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If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
- a)(P - Q)/R
- b)PQ - R
- c)PQ/R
- d)(PR - Q2)/R
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If P, Q, R are physical quantities, having different dimensions, which...
Physical quantities having different dimensions cannot be added or subtracted.
As P, Q and R are physical quantities having different dimensions, therefore they can neither be added nor be subtracted.
Thus, (a) can never be a meaningful quantity.
As P, Q and R are physical quantities having different dimensions, therefore they can neither be added nor be subtracted.
Thus, (a) can never be a meaningful quantity.
Most Upvoted Answer
If P, Q, R are physical quantities, having different dimensions, which...
Explanation:
To determine which combination can never be a meaningful quantity, we need to consider the dimensions of the quantities involved.
The dimensions of a physical quantity represent its physical nature and are usually expressed in terms of fundamental dimensions such as length, mass, time, etc.
Let's analyze each combination and determine their dimensions:
a) (P - Q)/R:
The dimensions of (P - Q) will be the same as the dimensions of P and Q since subtraction is only valid between quantities with the same dimensions. Therefore, the dimensions of (P - Q)/R will be the same as the dimensions of P and Q divided by the dimensions of R.
b) PQ - R:
The dimensions of PQ will be the product of the dimensions of P and Q. The dimensions of R will be the same as the dimensions of P and Q since subtraction is only valid between quantities with the same dimensions. Therefore, the dimensions of PQ - R will be the same as the dimensions of P and Q.
c) PQ/R:
The dimensions of PQ will be the product of the dimensions of P and Q. The dimensions of R will be the same as the dimensions of P and Q since division is only valid between quantities with the same dimensions. Therefore, the dimensions of PQ/R will be the same as the dimensions of P and Q divided by the dimensions of R.
d) (PR - Q^2)/R:
The dimensions of PR will be the product of the dimensions of P and R. The dimensions of Q^2 will be the square of the dimensions of Q. The dimensions of R will be the same as the dimensions of P and Q since subtraction and division are only valid between quantities with the same dimensions. Therefore, the dimensions of (PR - Q^2)/R will be the same as the dimensions of P and Q.
From the above analysis, we can conclude that the combination (P - Q)/R can never be a meaningful quantity because subtraction is only valid between quantities with the same dimensions. Therefore, the correct answer is option 'A'.
To determine which combination can never be a meaningful quantity, we need to consider the dimensions of the quantities involved.
The dimensions of a physical quantity represent its physical nature and are usually expressed in terms of fundamental dimensions such as length, mass, time, etc.
Let's analyze each combination and determine their dimensions:
a) (P - Q)/R:
The dimensions of (P - Q) will be the same as the dimensions of P and Q since subtraction is only valid between quantities with the same dimensions. Therefore, the dimensions of (P - Q)/R will be the same as the dimensions of P and Q divided by the dimensions of R.
b) PQ - R:
The dimensions of PQ will be the product of the dimensions of P and Q. The dimensions of R will be the same as the dimensions of P and Q since subtraction is only valid between quantities with the same dimensions. Therefore, the dimensions of PQ - R will be the same as the dimensions of P and Q.
c) PQ/R:
The dimensions of PQ will be the product of the dimensions of P and Q. The dimensions of R will be the same as the dimensions of P and Q since division is only valid between quantities with the same dimensions. Therefore, the dimensions of PQ/R will be the same as the dimensions of P and Q divided by the dimensions of R.
d) (PR - Q^2)/R:
The dimensions of PR will be the product of the dimensions of P and R. The dimensions of Q^2 will be the square of the dimensions of Q. The dimensions of R will be the same as the dimensions of P and Q since subtraction and division are only valid between quantities with the same dimensions. Therefore, the dimensions of (PR - Q^2)/R will be the same as the dimensions of P and Q.
From the above analysis, we can conclude that the combination (P - Q)/R can never be a meaningful quantity because subtraction is only valid between quantities with the same dimensions. Therefore, the correct answer is option 'A'.
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If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?a)(P - Q)/Rb)PQ - Rc)PQ/Rd)(PR - Q2)/RCorrect answer is option 'A'. Can you explain this answer?
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