On the basis of dimensions, decide which of the following relation for the displacement of a particle undergoing simple harmonic motion is not correct :

Options

A. `y = a sin (2pit)/T`
B. `y = a sin vt`
C. `y = a/T sin((t)/(a))`
D. `y=a sqrt(2) (sin(2pit)/T - cos (2pit)/T)`

Answer

B, C

Explanation

Now, by principle of homogeneity of dimensions LHS and RHS of (a) and (b) will be same and is L.
For c) [LHS] = L
[RHS] = `L/T = LT^(-1)`
`[LHS] ne [RHS]`
Hence c) is not correct option
In option (b) dimension of angle is [vt] i.e., L
`implies RHS =L.L=L^2 and LHS=L`
`implies LHS ne RHS`
So option (b) is also not correct