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

Options

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

Explanation

Now the dimension of LHS and RHS of (a) and (d) will be same and is `L^(1)`
For (c) [LHS] `=L^(1)`
`[RHS]=(L^(1))/(T^(1))=L^(1)T^(-1)`
`[LHS]ne [RHS]`
Hence, (c) is not correct option .
In option (b) dimension of angle `=[vt]=L^(1)`
Dimensions of RHS= `L^(1)L^(1)=L^(2)` and Dimensions of LHS `=L^(1)`
`:. [LHS] ne [RHS]`
So, option (b) is also not correct.