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 dimensions on both sides, `LHS = [M^(0) L^(1) T^(0)]`
`RHS = [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)]`
Comparing the `LHS and RHS` , we get
`LHS = RHS`
Hence the formula is dimensionally correct.