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(B) The damping force $F$ is given by the relation $F = -bv$,where $b$ is the constant of proportionality (damping constant) and $v$ is the velocity.T

Vedclass · Accepted Answer

$kg \cdot s^{-1}$

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(B) The damping force $F$ is given by the relation $F = -bv$,where $b$ is the constant of proportionality (damping constant) and $v$ is the velocity.To find the unit of $b$,we rearrange the formula: $b = \frac{F}{v}$.The $SI$ unit of force $F$ is Newton $(N)$,which is equivalent to $kg \cdot m \cdot s^{-2}$.The $SI$ unit of velocity $v$ is $m \cdot s^{-1}$.Substituting these units into the formula for $b$:$b = \frac{kg \cdot m \cdot s^{-2}}{m \cdot s^{-1}} = kg \cdot s^{-1}$.Therefore,the unit of the constant of proportionality is $kg \cdot s^{-1}$.

List-$I$	List-$II$
$(a)$ $h$ (Planck's constant)	$(i)$ $[M L T^{-1}]$
$(b)$ $E$ (kinetic energy)	$(ii)$ $[M L^2 T^{-1}]$
$(c)$ $V$ (electric potential)	$(iii)$ $[M L^2 T^{-2}]$
$(d)$ $P$ (linear momentum)	$(iv)$ $[M L^2 I^{-1} T^{-3}]$

The damping force of an oscillator is directly proportional to the velocity. The unit of the constant of proportionality is:

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