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}} )$
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}} )$
- A
$500$ $ \mu s$
- B
$50$ $ ms$
- C
$0.5$ $ s$
- D
$5 $ $ s$
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Mercury is filled in a tube of radius $2 \mathrm{~cm}$ up to a height of $30 \mathrm{~cm}$. The force exerted by mercury on the bottom of the tube is. . . . . . $\mathrm{N}$.
(Given, atmospheric pressure $=10^5 \mathrm{Nm}^{-2}$, density of mercury $=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^3, \mathrm{~g}=10 \mathrm{~ms}^2$, $\left.\pi=\frac{22}{7}\right)$
Mercury is filled in a tube of radius $2 \mathrm{~cm}$ up to a height of $30 \mathrm{~cm}$. The force exerted by mercury on the bottom of the tube is. . . . . . $\mathrm{N}$.
(Given, atmospheric pressure $=10^5 \mathrm{Nm}^{-2}$, density of mercury $=1.36 \times 10^4 \mathrm{~kg} \mathrm{~m}^3, \mathrm{~g}=10 \mathrm{~ms}^2$, $\left.\pi=\frac{22}{7}\right)$
- [JEE MAIN 2024]
An object falling through a fluid is observed to have acceleration given by $a = g -bv$ where $g =$ gravitational acceleration and $b$ is constant. After a long time of release, it is observed to fall with constant speed. The value of constant speed is
An object falling through a fluid is observed to have acceleration given by $a = g -bv$ where $g =$ gravitational acceleration and $b$ is constant. After a long time of release, it is observed to fall with constant speed. The value of constant speed is
Write $\mathrm{SI}$ and $\mathrm{CGS}$ unit of coefficient of viscosity.
Write $\mathrm{SI}$ and $\mathrm{CGS}$ unit of coefficient of viscosity.