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 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
$\sqrt {\frac{{Vg({\rho _1} - {\rho _2})}}{k}} $
- B
$\frac{{Vg{\rho _1}}}{k}$
- C
$\sqrt {\frac{{Vg{\rho _1}}}{k}} $
- D
$\frac{{Vg({\rho _1} - {\rho _2})}}{k}$
Similar Questions
A cubical block of side $‘a’$ and density ‘$\rho $’ slides over a fixed inclined plane with constant velocity $‘v’$. There is a thin film of viscous fluid of thickness $‘t’$ between the plane and the block. Then the coefficient of viscosity of the thin film will be
A cubical block of side $‘a’$ and density ‘$\rho $’ slides over a fixed inclined plane with constant velocity $‘v’$. There is a thin film of viscous fluid of thickness $‘t’$ between the plane and the block. Then the coefficient of viscosity of the thin film will be
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
The diagram below shows a hydraulic lift. A force is applied at side $1$ and an output force is generated at side $2$ . Which of the following is true?
The diagram below shows a hydraulic lift. A force is applied at side $1$ and an output force is generated at side $2$ . Which of the following is true?
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 ..........
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 ..........
A $U$ tube contains water and methylated spirit separated by mercury . The mercury columns in the two arms are at the same level with $10\,cm$ of water in one arm and $12.5\,cm$ of spirit in the other as shown in figure. The relative density of the spirit is
A $U$ tube contains water and methylated spirit separated by mercury . The mercury columns in the two arms are at the same level with $10\,cm$ of water in one arm and $12.5\,cm$ of spirit in the other as shown in figure. The relative density of the spirit is