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A physical quantity \( X \) depends on another physical quantities as \( X=Y F e^{-\beta r^{2}}+Z W \sin (\alpha r) \) where \( r, F \) and \( W \) represents distance,
\( \mathrm{P} \) force and work respectively and \( Y \) and \( Z \) are unknown physical quantities and \( \alpha, \beta \) are positive constants.
If \( Y \) represents velocity, then \( \operatorname{dim}(X) \) is equal to
(1) \( M L^{2} T^{-3} \)
(2) \( M^{-1} L^{2} T^{-3} \)
(3) \( M L^{2} T^{-2} \)
(4) None of these
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