00. Fluid Property (Pressure, Density), Viscosity
Mechanical Properties of Fluids

142766 A water drop of radius $1 \mu \mathrm{m}$ falls in a situation where the effect of buoyant force is negligible, Co-efficient of viscosity of air is $1.8 \times 10^{-5} \mathrm{Nsm}^{-2}$ and its density is negligible as compared to that of water $\left(10^{6} \mathrm{gm}^{-3}\right)$. Terminal velocity of the water drop is
(Take acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $145.4 \times 10^{-6} \mathrm{~ms}^{-1}$
2 $118.0 \times 10^{-6} \mathrm{~ms}^{-1}$
3 $132.6 \times 10^{-6} \mathrm{~ms}^{-1}$
4 $123.4 \times 10-^{6} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

142767 The velocity of a small ball of mass ' $m$ ' and density $d_{1}$ when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $d_{2}$, then the viscous force acting on the ball will be

1 $\operatorname{mg}\left(1-\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}\right)$
2 $\mathrm{mg}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right)$
3 $\mathrm{mg}\left(\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}-1\right)$
4 $\mathrm{mg}\left(\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}-1\right)$
Mechanical Properties of Fluids

142769 A vessel contains oil (density $0.8 \mathrm{~g} / \mathrm{cm}^{3}$ ) over mercury (density $13.6 \mathrm{~g} / \mathrm{cm}^{3}$ ) A homogeneous sphere floats with half volume immersed in mercury and the other half in oil. What will be the density (in $\mathrm{g} / \mathrm{cm}^{3}$ ) of the material of the sphere?

1 7.2
2 8.6
3 10.4
4 None of these
Mechanical Properties of Fluids

142770 The density of a liquid of coefficient of cubical expansion $\gamma$ is $\rho$ at $0^{\circ} \mathrm{C}$. When the liquid is heated to a temperature $T$, the change in density will be

1 $-\frac{\rho \gamma \mathrm{T}}{(1+\gamma \mathrm{T})}$
2 $\frac{\rho \gamma \mathrm{T}}{(1+\gamma \mathrm{T})}$
3 $-\frac{\rho(1+\gamma \mathrm{T})}{\gamma \mathrm{T}}$
4 $\frac{\rho(1-\gamma \mathrm{T})}{\gamma \mathrm{T}}$
Mechanical Properties of Fluids

142766 A water drop of radius $1 \mu \mathrm{m}$ falls in a situation where the effect of buoyant force is negligible, Co-efficient of viscosity of air is $1.8 \times 10^{-5} \mathrm{Nsm}^{-2}$ and its density is negligible as compared to that of water $\left(10^{6} \mathrm{gm}^{-3}\right)$. Terminal velocity of the water drop is
(Take acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $145.4 \times 10^{-6} \mathrm{~ms}^{-1}$
2 $118.0 \times 10^{-6} \mathrm{~ms}^{-1}$
3 $132.6 \times 10^{-6} \mathrm{~ms}^{-1}$
4 $123.4 \times 10-^{6} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

142767 The velocity of a small ball of mass ' $m$ ' and density $d_{1}$ when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $d_{2}$, then the viscous force acting on the ball will be

1 $\operatorname{mg}\left(1-\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}\right)$
2 $\mathrm{mg}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right)$
3 $\mathrm{mg}\left(\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}-1\right)$
4 $\mathrm{mg}\left(\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}-1\right)$
Mechanical Properties of Fluids

142769 A vessel contains oil (density $0.8 \mathrm{~g} / \mathrm{cm}^{3}$ ) over mercury (density $13.6 \mathrm{~g} / \mathrm{cm}^{3}$ ) A homogeneous sphere floats with half volume immersed in mercury and the other half in oil. What will be the density (in $\mathrm{g} / \mathrm{cm}^{3}$ ) of the material of the sphere?

1 7.2
2 8.6
3 10.4
4 None of these
Mechanical Properties of Fluids

142770 The density of a liquid of coefficient of cubical expansion $\gamma$ is $\rho$ at $0^{\circ} \mathrm{C}$. When the liquid is heated to a temperature $T$, the change in density will be

1 $-\frac{\rho \gamma \mathrm{T}}{(1+\gamma \mathrm{T})}$
2 $\frac{\rho \gamma \mathrm{T}}{(1+\gamma \mathrm{T})}$
3 $-\frac{\rho(1+\gamma \mathrm{T})}{\gamma \mathrm{T}}$
4 $\frac{\rho(1-\gamma \mathrm{T})}{\gamma \mathrm{T}}$
Mechanical Properties of Fluids

142766 A water drop of radius $1 \mu \mathrm{m}$ falls in a situation where the effect of buoyant force is negligible, Co-efficient of viscosity of air is $1.8 \times 10^{-5} \mathrm{Nsm}^{-2}$ and its density is negligible as compared to that of water $\left(10^{6} \mathrm{gm}^{-3}\right)$. Terminal velocity of the water drop is
(Take acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $145.4 \times 10^{-6} \mathrm{~ms}^{-1}$
2 $118.0 \times 10^{-6} \mathrm{~ms}^{-1}$
3 $132.6 \times 10^{-6} \mathrm{~ms}^{-1}$
4 $123.4 \times 10-^{6} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

142767 The velocity of a small ball of mass ' $m$ ' and density $d_{1}$ when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $d_{2}$, then the viscous force acting on the ball will be

1 $\operatorname{mg}\left(1-\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}\right)$
2 $\mathrm{mg}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right)$
3 $\mathrm{mg}\left(\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}-1\right)$
4 $\mathrm{mg}\left(\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}-1\right)$
Mechanical Properties of Fluids

142769 A vessel contains oil (density $0.8 \mathrm{~g} / \mathrm{cm}^{3}$ ) over mercury (density $13.6 \mathrm{~g} / \mathrm{cm}^{3}$ ) A homogeneous sphere floats with half volume immersed in mercury and the other half in oil. What will be the density (in $\mathrm{g} / \mathrm{cm}^{3}$ ) of the material of the sphere?

1 7.2
2 8.6
3 10.4
4 None of these
Mechanical Properties of Fluids

142770 The density of a liquid of coefficient of cubical expansion $\gamma$ is $\rho$ at $0^{\circ} \mathrm{C}$. When the liquid is heated to a temperature $T$, the change in density will be

1 $-\frac{\rho \gamma \mathrm{T}}{(1+\gamma \mathrm{T})}$
2 $\frac{\rho \gamma \mathrm{T}}{(1+\gamma \mathrm{T})}$
3 $-\frac{\rho(1+\gamma \mathrm{T})}{\gamma \mathrm{T}}$
4 $\frac{\rho(1-\gamma \mathrm{T})}{\gamma \mathrm{T}}$
Mechanical Properties of Fluids

142766 A water drop of radius $1 \mu \mathrm{m}$ falls in a situation where the effect of buoyant force is negligible, Co-efficient of viscosity of air is $1.8 \times 10^{-5} \mathrm{Nsm}^{-2}$ and its density is negligible as compared to that of water $\left(10^{6} \mathrm{gm}^{-3}\right)$. Terminal velocity of the water drop is
(Take acceleration due to gravity $=10 \mathrm{~ms}^{-2}$ )

1 $145.4 \times 10^{-6} \mathrm{~ms}^{-1}$
2 $118.0 \times 10^{-6} \mathrm{~ms}^{-1}$
3 $132.6 \times 10^{-6} \mathrm{~ms}^{-1}$
4 $123.4 \times 10-^{6} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

142767 The velocity of a small ball of mass ' $m$ ' and density $d_{1}$ when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is $d_{2}$, then the viscous force acting on the ball will be

1 $\operatorname{mg}\left(1-\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}\right)$
2 $\mathrm{mg}\left(1-\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}\right)$
3 $\mathrm{mg}\left(\frac{\mathrm{d}_{1}}{\mathrm{~d}_{2}}-1\right)$
4 $\mathrm{mg}\left(\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}-1\right)$
Mechanical Properties of Fluids

142769 A vessel contains oil (density $0.8 \mathrm{~g} / \mathrm{cm}^{3}$ ) over mercury (density $13.6 \mathrm{~g} / \mathrm{cm}^{3}$ ) A homogeneous sphere floats with half volume immersed in mercury and the other half in oil. What will be the density (in $\mathrm{g} / \mathrm{cm}^{3}$ ) of the material of the sphere?

1 7.2
2 8.6
3 10.4
4 None of these
Mechanical Properties of Fluids

142770 The density of a liquid of coefficient of cubical expansion $\gamma$ is $\rho$ at $0^{\circ} \mathrm{C}$. When the liquid is heated to a temperature $T$, the change in density will be

1 $-\frac{\rho \gamma \mathrm{T}}{(1+\gamma \mathrm{T})}$
2 $\frac{\rho \gamma \mathrm{T}}{(1+\gamma \mathrm{T})}$
3 $-\frac{\rho(1+\gamma \mathrm{T})}{\gamma \mathrm{T}}$
4 $\frac{\rho(1-\gamma \mathrm{T})}{\gamma \mathrm{T}}$
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