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 spherical body of mass $m$ and radius $r$ is allowed to fall in a medium of viscosity $\eta $. The time in which the velocity of the body increases from zero to $0.63\, times$ the terminal velocity $(v)$ is called time constant $\left( \tau  \right)$. Dimensionally $\tau $ can be represented by

A cubical block is floating in a liquid with half of its volume immersed in the liquid. When the whole system accelerates upwards with a net acceleration of $g/3$. The fraction of volume immersed in the liquid will be :-

Which of the following functions of $A$ and $B$ may be performed if $A$ and $B$ possess different dimensions

A lead shot of $1\, mm$ diameter falls through a long column of glycerine. The variation of its velocity $v$ with distance covered is represented by

A solid cylinder of mass $m$ and volume $v$ is suspended from ceiling by a spring of spring constant $k$ . It has cross-section area $A$ . It is submerged in a liquid of density $\rho $ upto half its length. If a small block of mass $M_o$ is kept at the centre of the top, the amplitude of small oscillation will be