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 2pi t//T`
B. `"y"=a sin vt`
C. `"y"=a/Tsin(t/a)`
D. `"y"=asqrt2(sin.(2pit)/T-cos.(2pit)/T)`

Answer

B, C

Explanation

Now, by principle of homogeneity of dimensions LHS and RHS of (a) and (d) 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
`Rightarrow RHS=L.L=L^(2)and LHS=L`
`Rightarrow LHSneRHS.`
So, option (b) is also not correct.