A book with many printing errors contains four different formulas for the displacement 
of a particle undergoing a certain periodic motion.
(I) 
(II) 
(III) 
(IV) 
(where, 
maximum displacement of the particle, 
speed of the particle, 
time period of motion). Which is the wrong formula on dimensional grounds?
Text Solution
Verified by ExpertsB
The dimension of LHS of each relation is [L].
I. As trigonometric term is dimensionless, therefore, dimensions of RHS 
. This formula is correct.
II. Dimension of RHS 
. As angle is not dimension less here. Therefore, this formula is wrong.
III. Dimension of RHS 
.
As angle is not dimensionless here, therefore this formula is wrong.
IV. Dimension of 
As angle is dimensionless and dimension of RHS is equal to the dimension of LHS, therefore this formula is correct.
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