The terminal velocity of a copper ball of radius $5\,mm$ falling through a tank of oil at room temperature is $10\,cm\,s ^{-1}$. If the viscosity of oil at room temperature is $0.9\,kg\,m ^{-1} s ^{-1}$, the viscous drag force is :
$8.48 \times 10^{-3}\,N$
$8.48 \times 10^{-5}\,N$
$4.23 \times 10^{-3}\,N$
$4.23 \times 10^{-6}\,N$
A lead shot of $1mm$ diameter falls through a long column of glycerine. The variation of its velocity $v$. with distance covered is represented by
Sixty four spherical rain drops of equal size are falling vertically through air with terminal velocity $1.5\, m/s$. All of the drops coalesce to form a big spherical drop, then terminal velocity of big drop is ........... $m/s$
A spherical ball of density $\rho$ and radius $0.003$ $m$ is dropped into a tube containing a viscous fluid filled up to the $0$ $ cm$ mark as shown in the figure. Viscosity of the fluid $=$ $1.260$ $N.m^{-2}$ and its density $\rho_L=\rho/2$ $=$ $1260$ $kg.m^{-3}$. Assume the ball reaches a terminal speed by the $10$ $cm$ mark. The time taken by the ball to traverse the distance between the $10$ $cm$ and $20$ $cm$ mark is
( $g$ $ =$ acceleration due to gravity $= 10$ $ ms^{^{-2}} )$
Eight spherical rain drops of the same mass and radius are falling down with a terminal speed of $6\, cm -s^{-1}$ . If they coalesce to form one big drop, what will be the terminal speed of the bigger drop ? (Neglect the buoyancy of the air) ....... $cm -s^{-1}$
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).