The force due to the right liquid comes out to be 3/2*rho*g*R^2*l (from integration).So we can see the pressure = 3/2*rho*g*R and area = R*l. so i think we can conclude that surface to be a cuboid of dimensions R*R*l
If you try to change the surface you still have to find the relation between the force on curved surface and any other surface.So I think there is no way without integration.
o,made silly mistakes.
\frac{dv}{dt}=\frac{k}{m}(\frac{D}{sinθ}-D)cosθ + g
now what to do after this?Should we consider a small change in θ and integrate it over the "θ" range to find the velocity??
So i should write it as:
F=k(D/sinθ -3) ... D =horizontal distance
so putting this value in first equation:
ma=Fcosθ + mg
ma=k(D/sinθ-3)cosθ + mg
dv/dt = k/m(D/sinθ-3)cosθ + g
\frac{dv}{dt}=\frac{k}{m}(\frac{D}{sinθ}-3)+g
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