A sphere of mass $M$ and radius $R$ is falling in a viscous fluid. The terminal velocity attained by the falling object will be proportional to
$R^2$
$R$
$1/R$
$1/R^2$
If the terminal speed of a sphere of gold (density $= 19.5 \times 10^3\, kg/m^3$) is $0.2\, m/s$ in a viscous liquid (density $= 1.5 \times 10^3\, kg/m^3$), find the terminal speed of a sphere of silver (density $= 10.5 \times 10^3\, kg/m^3$) of the same size in the same liquid ........... $m/s$
The height to which a cylindrical vessel be filled with a homogeneous liquid, to make the average force with which the liquid presses the side of the vessel equal to the force exerted by the liquid on the bottom of the vessel, is equal to
A tank is filled upto a height $h$ with a liquid and is placed on a platform of height $h$ from the ground. To get maximum range $x_m$ a small hole is punched at a distance of $y$ from the free surface of the liquid. Then
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., $F_{viscous} = -k\upsilon ^2 (k > 0)$. The terminal speed of the ball is
A pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. A container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it’s balanced. A brass weight on the end of a string is then lowered into the water, but not allowed to rest on the bottom of the container. What happens next?