Physics

# A book with many printing errors contains four different expressions for the displacement y of a particle executing simple harmonic motion. The wrong formula on dimensional basis is/are:i. $y=A \sin{(Vt)}$ii. $y=\dfrac{A}{T} \sin{(\dfrac{t}{A})}$  iii. $y= \dfrac { A }{ \sqrt { 2 } } \left( sin(wt)+cos(wt) \right)$

i and ii only

##### SOLUTION
Given physical expression is dimensionally correct only when RHS and LHS has same dimensions.
Also in trigonometry expression the term inside a trigonometry function should be dimensionless.
Therefore expression 1 is wrong because Vt has dimension of length.
Similarly expression 2.

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Single Correct Medium Published on 18th 08, 2020
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