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Question: Answered & Verified by Expert
Assertion (A) Energy per unit volume and angular momentum can be added dimensionally.
Reason (R) Physical quantities having same dimensions can be added or subtracted.
PhysicsUnits and DimensionsAP EAMCETAP EAMCET 2018 (23 Apr Shift 1)
Options:
  • A Both (A) and (R) are true and (R) is the correct explanation of (A)
  • B Both (A) and (R) are true but (R) is not the correct explanation of (A)
  • C (A) is true but (R) is false
  • D (A) is false but (R) is true
Solution:
1568 Upvotes Verified Answer
The correct answer is: (A) is false but (R) is true
The units of energy per unit volume is $\mathrm{J} / \mathrm{m}^3$ or $\mathrm{kg} / \mathrm{m}-\mathrm{s}^2$ and that for angular momentum is $\mathrm{kg}-\mathrm{m}^2 / \mathrm{s}$.
Since, they are not dimensionally equal, they cannot be added, so the Assertion (A) is false. Only those physical quantities that have same dimensions can be added or subtracted, so Reason (R) is true.
Hence, the correct option is $(\mathrm{d})$.

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