Using dimensional analysis, check the correctness of the following relations : (i) `S_(nth) = u+(a)/(2) (2n-1)` (ii) `lambda = h//m upsilon` (ii) ` = mc^2` where the symbole have their usual menaings.]

Answer

All the three relation are correct

Explanation

(i) Refer to solved Example 9, Page 1//67.
(ii) `lambda = h//m upsilon`
`LHS = lambda = [L]`
`RHS = (h)/(m upsilon) = (ML^2T^(-1))/(MLT^(-1)) = [L]`
The relation is dimensionally correct.
(iii) `E = mc^2`
`LHS = E = [M^1L^2 T^(-2)]`
`RHS =mc^2 = M(LT^(-1))^2 = [M^1L^2 T^(-2)]`
The relation is dimensinally correct.