InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If momentum `(p)`, area `(A)` and time`(t) `are taken to be fundamental quantities then energy has the dimensional formulaA. `[p^(1)A^(-1)t^(-1)]`B. `[p^(2)A^(1)t^(1)]`C. `[p^(1)A^(1//2)t^(1)]`D. `[p^(1)A^(1//2)t^(-1)]` |
|
Answer» Correct Answer - d Let enegry `E = kp^(a) A^(b)t^(c )`…(i) where is k a dimensionless constant proportionality equating dimension an both sides of(i) we get `[ML^(2)T^(-2)] = [MLT^(-1)]^(a) [M^(0)L^(2)T^(0)]^(b) [M^(0)L(0)T]^(c)` `[L]= [M^(a)L^(a+2b)T^(a+c)]` Appliying the principle of homogenety of dimensions we get `a = 1`...(ii) `a + 2b = 2`...(iii) `-a+c = -2`...(iv) On solving eqs `(ii),(iii)` and `(iv)` we get `a = 1, b = (1)/(2) , c=-1` `:. [E] = [p^(1)A^(1//2)c^(-2)]` |
|