A cylindrical vessel filled with water is released on an inclined surface of angle $\theta$ as shown in figure.The friction coefficient of surface with vessel is $\mu( < \tan \theta)$.Then the contact angle made by the surface of water with the incline will be

Two drops of same radius are falling through air with steady velocity of $v $ $cm/s$. If the two drops coalesce, what would be the terminal velocity?

Small water droplets of radius $0.01 \mathrm{~mm}$ are formed in the upper atmosphere and falling with a terminal velocity of $10 \mathrm{~cm} / \mathrm{s}$. Due to condensation, if $8 \mathrm{such}$ droplets are coalesced and formed a larger drop, the new terminal velocity will be ........... $\mathrm{cm} / \mathrm{s}$.

Spherical balls of radius $ 'r'$  are falling in a viscous fluid of viscosity '$\eta$' with a velocity $ 'v'. $ The retarding viscous force acting on the spherical ball is

When a body falls in air, the resistance of air depends to a great extent on the shape of the body, $ 3 $ different shapes are given. Identify the combination of air resistances which truly represents the physical situation. (The cross sectional areas are the same).

A water drop of radius $1\,\mu m$ falls in a situation where the effect of buoyant force is negligible. Coefficient of viscosity of air is $1.8 \times 10^{-5}\,Nsm ^{-2}$ and its density is negligible as compared to that of water $10^{6}\,gm ^{-3}$. Terminal velocity of the water drop is________ $\times 10^{-6}\,ms ^{-1}$

(Take acceleration due to gravity $=10\,ms ^{-2}$ )