A book with many printing errors contains four different formulae for the displacement y of a particle undergoing a certain periodic motion.
1. `y= asin""(2pit)/(T)`
2. `y= asinvt`
3. `y= (a)/(T)sin""(t)/(a)`
4. `y= (asqrt(2))(sin((2pit)/(T))+ cos((2pit)/(T)))`
where a is the maximum displacement of the particle, v is the speed of the particle, T is the time period of motion. Then dimensionally

Options

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

Answer

B

Explanation

Since LHS is displacement, so RHS should have dimensions of displacement. Also argument of a trigonometric function should be dimensionless. In (2) argument is not dimensionless. In (3) argument is not dimensionless and `(a)/(T)` has not dimension of displacement. Therefore (2) and (3) are dimensionally wrong.