Three physical quantities A, B and C are related as A = B + C, then
1)Dimensions of A, B and C are same
2)Dimensions of A, B and C are different
3)Dimensions of A and B are same but dimensions of A and C are different
4)Dimensions of B and C are same but dimensions of A and C are different
please answer with explanation
Answers
Option (1) : The dimensions of A, B and C are same
Explanation: The dimensions of B and C are same because the dimensions that are completely same can be added. Unlike dimensions are not added, they can be only multiplied.
For example, let dimensions of B be M and dimensions of C be also M. These can be added.
But, let dimensions of B be M and dimensions of C be L. These cannot be added since mass and length of an object are not additive.
Now, when B and C of same dimensions are added, the sum is also of same dimensions. For example, when two masses 4 kg and 6 kg are added, the resulting sum 10 kg also is a measure of mass.
Therefore, A also has the same dimensions as that of B and C.
This proves that A, B and C have the same dimensions.
Three physical quantities A, B and C are related as A = B + C, then Dimensions of A, B and C are same
A = B + C
Linear operations can be performed on Quantities with same dimensions only.
Linear operations are Addition and subtraction.
Here B + C is linear operation on B and C
Hence B and C must have Same dimensions.
Dimensions does not change on linear operation.
Hence Dimensions of B + C will be same as of B and C
Quantities can be compared/equated only if they have same dimensions.
Hence Dimension A of will be same as of B + C
Hence Dimensions of A , B and C are same
Only option 1) has Dimensions of A , B and C same so correct option is 1).
Three physical quantities A, B and C are related as A = B + C, then Dimensions of A, B and C are same
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