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(A) The terminal velocity $v$ of a spherical body of radius $r$ and density $\rho$ falling through a fluid of density $\sigma$ and viscosity $\eta$ is

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Straight line with positive slope

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(A) The terminal velocity $v$ of a spherical body of radius $r$ and density $\rho$ falling through a fluid of density $\sigma$ and viscosity $\eta$ is given by Stokes' Law:$v = \frac{2}{9} \frac{r^2 g (\rho - \sigma)}{\eta}$Here,$g$ is the acceleration due to gravity and $\eta$ is the coefficient of viscosity.We are plotting $v$ (on the $y-$ axis) against $r^2$ (on the $x-$ axis).Let $y = v$ and $x = r^2$.The equation becomes $y = \left( \frac{2g(\rho - \sigma)}{9\eta} \right) x$.This is of the form $y = mx$,which represents a straight line passing through the origin with a positive slope $m = \frac{2g(\rho - \sigma)}{9\eta}$ (assuming $\rho > \sigma$ for the body to fall).Therefore,the graph is a straight line with a positive slope.

The graph between terminal velocity (along $y-$ axis) and square of radius (along $x-$ axis) of a spherical body of density $\rho$ allowed to fall through a fluid of density $\sigma$ is a

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