If the terminal speed of a sphere of gold (density $= 19.5\, kg/m^3$ ) is $0.2\, m/s$ in a viscous liquid (density $= 1.5\, kg/m^3$ ), find the terminal speed of a sphere of silver (density $=10.5\, kg/m^3$ ) of the same size in the same liquid …….. $m/s$

A cylindrical vessel filled with water upto the height $H$ becomes empty in time $t_0$ due to a small hole at the bottom of the vessel. If water is filled to a height $4H$ it will flow out in time

What is the pressure on a swimmer $20 \,m$ below the surface of water is ….. $atm$

A spherical solid ball of volume $V$ is made of a material of density $\rho _1$ . It is falling through a liquid of density $\rho _2(\rho _2 < \rho _1)$ . Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$ , i.e., $F_{viscous} =\, -kv^2 (k > 0)$ . Then terminal speed of the ball is

A large open tank has two holes in its wall. One is a square of side $a$ at a depth $x$ from the top and the other is a circular hole of radius $r$ at depth $4 x$ from the top. When the tank is completely filled with water, the quantities of water flowing out per second from both holes are the same. Then $r$ is equal to ……….