A spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_1 (\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous} = -kv^2 (k > 0)$. The terminal speed of the ball is
A spherical solid ball of volume $V$ is made of a material of density $\rho_1$. It is falling through a liquid of density $\rho_1 (\rho_2 < \rho_1)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{viscous} = -kv^2 (k > 0)$. The terminal speed of the ball is
- A
$\sqrt {\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}}$
- B
$\frac{{Vg{\rho _1}}}{k}$
- C
$\sqrt {\frac{{Vg{\rho _1}}}{k}}$
- D
$\frac{{Vg\left( {{\rho _1} - {\rho _2}} \right)}}{k}$
Similar Questions
For a constant hydraulic stress on an object, the fractional change in the object’s volume $(\Delta V/V)$ and its bulk modulus $(B)$ are related as
For a constant hydraulic stress on an object, the fractional change in the object’s volume $(\Delta V/V)$ and its bulk modulus $(B)$ are related as
Two equal drops are falling through air with a steady velocity of $5\, cm/second$. If two drops coalesce to form one drop then new terminal velocity will be
Two equal drops are falling through air with a steady velocity of $5\, cm/second$. If two drops coalesce to form one drop then new terminal velocity will be
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 :-
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 :-
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
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
A homogeneous solid cylinder of length $L(L < H/2)$, cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure $P_0$. Then, density $D$ of solid is given by
A homogeneous solid cylinder of length $L(L < H/2)$, cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the figure. The lower density liquid is open to atmosphere having pressure $P_0$. Then, density $D$ of solid is given by