[tex]\huge{\red{\sf{QUESTION:-}}}[/tex]
The velocity of a particle is given
[tex]v = \alpha \sin(wt) + \beta {e}^{ - 2t} [/tex]
where t is time and
[tex] \alpha [/tex]
and
[tex] \beta [/tex]
are dimensional constants. The unit of
[tex] \alpha \beta [/tex]
is
options:-
1) ms-¹
2) m²s²
3) m²s-²
4) ms-²
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[tex]\colorbox{lightgreen} {\red★ANSWER }[/tex]
To determine the unit of,
[tex](\alpha \beta)[/tex]
let's analyze the given expression for velocity:
[tex]\[v = \alpha \sin(wt) + \beta e^{-2t}\][/tex]
Since velocity is expressed in units of length over time (e.g., meters per second), we need to ensure that the coefficients \(\alpha\) and \(\beta\) result in the same unit when multiplied.
The unit of \(\alpha\) would be the unit of velocity divided by the unit of \(\sin(wt)\), and the unit of \(\beta\) would be the unit of velocity divided by the unit of \(e^{-2t}\).
Therefore, the unit of \(\alpha \beta\) would be the product of these units, which is the unit of velocity squared.
Among the given options, the correct one is:
2) \(m^2s^2\)