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Which of the following has dimensions different from the other three- √(LC) RC L/R LR

Which of the following has dimensions different from the other three-
  1. √(LC)
  2. RC
  3. L/R
  4. LR

Grade:11

1 Answers

Arun
25763 Points
2 years ago
First of all we have to find out dimension of L and R .
We know, relation L answer energy is E = 1/2Li² 
so, dimension of L = dimension of energy/dimension of i²
= [ML²T⁻²]/[A²] = [ML²T⁻²A⁻²] 
Similarly we know, relation between R and energy is E = i²Rt 
So, dimension of R = dimension of E/dimension of i²t
= [ML²T⁻²][A²T] = [ML²T⁻³A⁻²]
Now, dimension of L/R = dimension of L/dimension of R 
= [ML²T⁻²A⁻²][ML²T⁻³A⁻²] = [T] 
 
 
Also RC and sqrt(LC) has also dimension as [T]
 
hence option D is correct answer

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