A small steel ball falls through a syrup at constant speed of $10 \mathrm{cm} {\mathrm{s}}^{-1}$. If the steel ball is pulled upwards with a force equal to twice its effective weight, how fast will it move upwards?

Two spheres $P$ and $Q$ of equal radii have densities ${\mathrm{\rho }}_1$ and ${\mathrm{\rho }}_2$, respectively. The spheres are connected by a massless string and placed in liquids $L_1$ and $L_2$ of densities ${\mathrm{\sigma }}_1$ and ${\mathrm{\sigma }}_2$ viscosities ${\mathrm{\eta }}_1$ and ${\mathrm{\eta }}_2$, respectively. They float in equilibrium with the sphere $P$ in $L_1$ and sphere $Q$ in $L_2$ and the string is being taut (see figure). If sphere $P$ alone in $L_2$ has terminal velocity ${\stackrel{\mathit{\rightharpoonup }}{\mathit{V}}}_{\mathit{P}}$ and $Q$ alone in $L_1$ has terminal velocity ${\stackrel{\mathit{\rightharpoonup }}{\mathit{V}}}_{\mathit{Q}}$, then

$F=-\eta A\frac{dv}{dx}$

where $\eta =$ coefficient of viscosity, so dimensions of $\eta$ will be :

The diagram shows a cup of tea seen from above. The tea has been stirred and is now rotating without turbulence. A graph showing the speed $v$ with which the liquid is crossing points at a distance $\mathrm{X}$ from $\mathrm{O}$ along a radius $\mathrm{XO}$ would look like

The radii of the two columns in a $U$-tube are $r_1$ and $r_2$. When a liquid of density '$P$' (angle of contact is $0°$) is filled in it, the level difference of the liquid in the two arms is '$h$'. The surface tension of the liquid is :

( $g$- accelaration due to gravity)