An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum velocities of fluid in this pipe is :

A solid sphere, of radius R acquires a terminal velocity v₁ when falling (due to gravity) through a viscous fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres. If each of these spheres acquires a terminal velocity, v₂, when falling through the same fluid, the ratio (v₁/v₂) equals :

The number density of molecules of a gas depends on their distance r from the origin as, $$n\left( r \right) = {n_0}{e^{ - \alpha {r^4}}}$$. Then the total number of molecules is proportional to :

A uniform cylindrical rod of length L and radius r, is made from a material whose Young’s modulus of Elasticity equals Y. When this rod is heated by temperature T and simultaneously subjected to a net longitudinal compressional force F, its length remains unchanged. The coefficient of volume expansion, of the material of the rod, is (nearly) equal to :