Question

Check whether the relation `S = ut + (1)/(2) at^(2)` is dimensionally correct or not , where symbols have their usual meaning .

Answer 1

We have `S = ut + (1)/(2) at^(2)`.checking the dimensoins on both sides, `LHS = [S] = [M^(@) L^(1) T^(0)]`
`RHS = [ut] + [(1)/(2) at^(2)] =m [LT^(1)][T] + [LT^(-2) [T^(2)]`
`= [M^(0) L^(1) T^(0)] + [M^(0) L^(1) T^(0)] = [M^(0) L^(1) T^(0)]`
We find `LHS + RHS`
Hence, the formula is dimensionally correct.