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Out of the formulae y =a sin 2pi t//T an...

Out of the formulae y =a sin `2pi t//T` and y = a sin `upsilon t` for the displacement y of particle undergoing a periodic motion, rule out the wrong formula on the basis of dimensions. Symbols have standard meaning.

Text Solution

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(i) `y = a sin(2pi t)/(T)`
`LHS =y = [L]:`
`RHS = a sin(2pi t)/(T) = L sin (T)/(T) = [L]`
As dimensions on both sides are same, this
formula is correct.
(ii) `y = a sin upsilon t`
LHS = y = [L],
`RHS =a sin upsilon t = L sin (LT^(-1). T) = L sin L`
As angle has to be dimensionless, this formula is wrong.
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