A student writes four different expression for the displacement `y` in a period motion
`y = a sin"(2 pi r)/(T)`
`y = a sin vt`
`y = (a)/(t) sin"(t)/(a)`
`y = (a )/(sqrt(2))[sin'(2 pi r)/(T)+ cos '(2 pi r)/(T)]`
where `a` is maximum displacement , x is the speed and T is the time period then dimensionally.

Options

A. 1 and 2 are wrong
B. 2 and 3 are wrong
C. 3 and 4 are wrong
D. 4 and 1 are wrong

Answer

b

Explanation

Since LHS is displacement, so RHS should have dimensions of displacementAlso argument of a trigonomentric function should be dimensions in equation (2) argamant is not dimensions and in equation (3) `a//T` has not the dimensions of displacement.