03. Excess of Pressure (Bubbles and Drops)
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Mechanical Properties of Fluids

143013 Two soap bubbles of radii $3 \mathrm{~mm}$ and $4 \mathrm{~mm}$ confined in vacuum coalesce isothermally to form a new bubble. The radius of the bubble formed (in mm) is

1 3
2 3.5
3 4
4 5
5 7
Kerala CEE -2018
Mechanical Properties of Fluids

143014 Two soap bubbles each with radius $r_{1}$ and $r_{2}$ coalesce in vacuum under isothermal conditions to form a bigger bubble of radius $R$. then, $R$ is equal to

1 $\sqrt{r_{1}^{2}+r_{2}^{2}}$
2 $\sqrt{r_{1}^{2}-r_{2}^{2}}$
3 $\mathrm{r}_{1}+\mathrm{r}_{2}$
4 $\frac{\sqrt{\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}}}{2}$
5 $2 \sqrt{r_{1}^{2}+r_{2}^{2}}$
CGPET 2005
Mechanical Properties of Fluids

143015 A ball of radius $r$ and density $\rho$ falls freely under gravity through a distance $h$ before entering water. Velocity of ball does not change even on entering water. If viscosity of water is $\eta$ the value of $h$ is given by

1 $\frac{2}{9} r^{2}\left(\frac{1-\rho}{\eta}\right) g$
2 $\frac{2}{81} r^{2}\left(\frac{\rho-1}{\eta}\right) g$
3 $\frac{2}{81} r^{4}\left(\frac{\rho-1}{\eta}\right)^{2} g$
4 $\frac{2}{9} r^{4}\left(\frac{\rho-1}{\eta}\right)^{2} g$
AIIMS-27.05.2018(M)
Mechanical Properties of Fluids

143016 A spherical solid ball of volume $V$ is made of a material of density $\rho_{1}$. It is falling through a liquid of density $\rho_{1}\left(\rho_{2} \lt \rho_{1}\right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{\text {viscous }}=-\mathbf{k v}_{\mathbf{t}}{ }^{2}(k>0)$. The terminal speed of the ball is

1 $\sqrt{\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}}$
2 $\frac{\mathrm{Vg} \rho_{1}}{\mathrm{k}}$
3 $\sqrt{\frac{\operatorname{Vg} \rho_{1}}{\mathrm{k}}}$
4 $\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}$
AIIMS-2013
Mechanical Properties of Fluids

143017 If the terminal speed of a sphere of gold (density $=19.5 \mathrm{~kg} / \mathrm{m}^{3}$ ) is $0.2 \mathrm{~m} / \mathrm{s}$ in a viscous liquid (density $=1.5 \mathrm{~kg} / \mathrm{m}^{3}$ ), find the terminal speed of a sphere of silver (density $=10.5$ $\mathrm{kg} / \mathrm{m}^{3}$ ) of the same size in the same liquid.

1 $0.4 \mathrm{~m} / \mathrm{s}$
2 $0.133 \mathrm{~m} / \mathrm{s}$
3 $0.1 \mathrm{~m} / \mathrm{s}$
4 $0.2 \mathrm{~m} / \mathrm{s}$
AIIMS-2008
NEET DIGITAL LIBRARY
Mechanical Properties of Fluids

143013 Two soap bubbles of radii $3 \mathrm{~mm}$ and $4 \mathrm{~mm}$ confined in vacuum coalesce isothermally to form a new bubble. The radius of the bubble formed (in mm) is

1 3
2 3.5
3 4
4 5
5 7
Kerala CEE -2018
Mechanical Properties of Fluids

143014 Two soap bubbles each with radius $r_{1}$ and $r_{2}$ coalesce in vacuum under isothermal conditions to form a bigger bubble of radius $R$. then, $R$ is equal to

1 $\sqrt{r_{1}^{2}+r_{2}^{2}}$
2 $\sqrt{r_{1}^{2}-r_{2}^{2}}$
3 $\mathrm{r}_{1}+\mathrm{r}_{2}$
4 $\frac{\sqrt{\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}}}{2}$
5 $2 \sqrt{r_{1}^{2}+r_{2}^{2}}$
CGPET 2005
Mechanical Properties of Fluids

143015 A ball of radius $r$ and density $\rho$ falls freely under gravity through a distance $h$ before entering water. Velocity of ball does not change even on entering water. If viscosity of water is $\eta$ the value of $h$ is given by

1 $\frac{2}{9} r^{2}\left(\frac{1-\rho}{\eta}\right) g$
2 $\frac{2}{81} r^{2}\left(\frac{\rho-1}{\eta}\right) g$
3 $\frac{2}{81} r^{4}\left(\frac{\rho-1}{\eta}\right)^{2} g$
4 $\frac{2}{9} r^{4}\left(\frac{\rho-1}{\eta}\right)^{2} g$
AIIMS-27.05.2018(M)
Mechanical Properties of Fluids

143016 A spherical solid ball of volume $V$ is made of a material of density $\rho_{1}$. It is falling through a liquid of density $\rho_{1}\left(\rho_{2} \lt \rho_{1}\right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{\text {viscous }}=-\mathbf{k v}_{\mathbf{t}}{ }^{2}(k>0)$. The terminal speed of the ball is

1 $\sqrt{\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}}$
2 $\frac{\mathrm{Vg} \rho_{1}}{\mathrm{k}}$
3 $\sqrt{\frac{\operatorname{Vg} \rho_{1}}{\mathrm{k}}}$
4 $\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}$
AIIMS-2013
Mechanical Properties of Fluids

143017 If the terminal speed of a sphere of gold (density $=19.5 \mathrm{~kg} / \mathrm{m}^{3}$ ) is $0.2 \mathrm{~m} / \mathrm{s}$ in a viscous liquid (density $=1.5 \mathrm{~kg} / \mathrm{m}^{3}$ ), find the terminal speed of a sphere of silver (density $=10.5$ $\mathrm{kg} / \mathrm{m}^{3}$ ) of the same size in the same liquid.

1 $0.4 \mathrm{~m} / \mathrm{s}$
2 $0.133 \mathrm{~m} / \mathrm{s}$
3 $0.1 \mathrm{~m} / \mathrm{s}$
4 $0.2 \mathrm{~m} / \mathrm{s}$
AIIMS-2008
Join With Us for More Updates
Mechanical Properties of Fluids

143013 Two soap bubbles of radii $3 \mathrm{~mm}$ and $4 \mathrm{~mm}$ confined in vacuum coalesce isothermally to form a new bubble. The radius of the bubble formed (in mm) is

1 3
2 3.5
3 4
4 5
5 7
Kerala CEE -2018
Mechanical Properties of Fluids

143014 Two soap bubbles each with radius $r_{1}$ and $r_{2}$ coalesce in vacuum under isothermal conditions to form a bigger bubble of radius $R$. then, $R$ is equal to

1 $\sqrt{r_{1}^{2}+r_{2}^{2}}$
2 $\sqrt{r_{1}^{2}-r_{2}^{2}}$
3 $\mathrm{r}_{1}+\mathrm{r}_{2}$
4 $\frac{\sqrt{\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}}}{2}$
5 $2 \sqrt{r_{1}^{2}+r_{2}^{2}}$
CGPET 2005
Mechanical Properties of Fluids

143015 A ball of radius $r$ and density $\rho$ falls freely under gravity through a distance $h$ before entering water. Velocity of ball does not change even on entering water. If viscosity of water is $\eta$ the value of $h$ is given by

1 $\frac{2}{9} r^{2}\left(\frac{1-\rho}{\eta}\right) g$
2 $\frac{2}{81} r^{2}\left(\frac{\rho-1}{\eta}\right) g$
3 $\frac{2}{81} r^{4}\left(\frac{\rho-1}{\eta}\right)^{2} g$
4 $\frac{2}{9} r^{4}\left(\frac{\rho-1}{\eta}\right)^{2} g$
AIIMS-27.05.2018(M)
Mechanical Properties of Fluids

143016 A spherical solid ball of volume $V$ is made of a material of density $\rho_{1}$. It is falling through a liquid of density $\rho_{1}\left(\rho_{2} \lt \rho_{1}\right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{\text {viscous }}=-\mathbf{k v}_{\mathbf{t}}{ }^{2}(k>0)$. The terminal speed of the ball is

1 $\sqrt{\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}}$
2 $\frac{\mathrm{Vg} \rho_{1}}{\mathrm{k}}$
3 $\sqrt{\frac{\operatorname{Vg} \rho_{1}}{\mathrm{k}}}$
4 $\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}$
AIIMS-2013
Mechanical Properties of Fluids

143017 If the terminal speed of a sphere of gold (density $=19.5 \mathrm{~kg} / \mathrm{m}^{3}$ ) is $0.2 \mathrm{~m} / \mathrm{s}$ in a viscous liquid (density $=1.5 \mathrm{~kg} / \mathrm{m}^{3}$ ), find the terminal speed of a sphere of silver (density $=10.5$ $\mathrm{kg} / \mathrm{m}^{3}$ ) of the same size in the same liquid.

1 $0.4 \mathrm{~m} / \mathrm{s}$
2 $0.133 \mathrm{~m} / \mathrm{s}$
3 $0.1 \mathrm{~m} / \mathrm{s}$
4 $0.2 \mathrm{~m} / \mathrm{s}$
AIIMS-2008
For More Updates join with Us
Mechanical Properties of Fluids

143013 Two soap bubbles of radii $3 \mathrm{~mm}$ and $4 \mathrm{~mm}$ confined in vacuum coalesce isothermally to form a new bubble. The radius of the bubble formed (in mm) is

1 3
2 3.5
3 4
4 5
5 7
Kerala CEE -2018
Mechanical Properties of Fluids

143014 Two soap bubbles each with radius $r_{1}$ and $r_{2}$ coalesce in vacuum under isothermal conditions to form a bigger bubble of radius $R$. then, $R$ is equal to

1 $\sqrt{r_{1}^{2}+r_{2}^{2}}$
2 $\sqrt{r_{1}^{2}-r_{2}^{2}}$
3 $\mathrm{r}_{1}+\mathrm{r}_{2}$
4 $\frac{\sqrt{\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}}}{2}$
5 $2 \sqrt{r_{1}^{2}+r_{2}^{2}}$
CGPET 2005
Mechanical Properties of Fluids

143015 A ball of radius $r$ and density $\rho$ falls freely under gravity through a distance $h$ before entering water. Velocity of ball does not change even on entering water. If viscosity of water is $\eta$ the value of $h$ is given by

1 $\frac{2}{9} r^{2}\left(\frac{1-\rho}{\eta}\right) g$
2 $\frac{2}{81} r^{2}\left(\frac{\rho-1}{\eta}\right) g$
3 $\frac{2}{81} r^{4}\left(\frac{\rho-1}{\eta}\right)^{2} g$
4 $\frac{2}{9} r^{4}\left(\frac{\rho-1}{\eta}\right)^{2} g$
AIIMS-27.05.2018(M)
Mechanical Properties of Fluids

143016 A spherical solid ball of volume $V$ is made of a material of density $\rho_{1}$. It is falling through a liquid of density $\rho_{1}\left(\rho_{2} \lt \rho_{1}\right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{\text {viscous }}=-\mathbf{k v}_{\mathbf{t}}{ }^{2}(k>0)$. The terminal speed of the ball is

1 $\sqrt{\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}}$
2 $\frac{\mathrm{Vg} \rho_{1}}{\mathrm{k}}$
3 $\sqrt{\frac{\operatorname{Vg} \rho_{1}}{\mathrm{k}}}$
4 $\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}$
AIIMS-2013
Mechanical Properties of Fluids

143017 If the terminal speed of a sphere of gold (density $=19.5 \mathrm{~kg} / \mathrm{m}^{3}$ ) is $0.2 \mathrm{~m} / \mathrm{s}$ in a viscous liquid (density $=1.5 \mathrm{~kg} / \mathrm{m}^{3}$ ), find the terminal speed of a sphere of silver (density $=10.5$ $\mathrm{kg} / \mathrm{m}^{3}$ ) of the same size in the same liquid.

1 $0.4 \mathrm{~m} / \mathrm{s}$
2 $0.133 \mathrm{~m} / \mathrm{s}$
3 $0.1 \mathrm{~m} / \mathrm{s}$
4 $0.2 \mathrm{~m} / \mathrm{s}$
AIIMS-2008
NEET DIGITAL LIBRARY
Mechanical Properties of Fluids

143013 Two soap bubbles of radii $3 \mathrm{~mm}$ and $4 \mathrm{~mm}$ confined in vacuum coalesce isothermally to form a new bubble. The radius of the bubble formed (in mm) is

1 3
2 3.5
3 4
4 5
5 7
Kerala CEE -2018
Mechanical Properties of Fluids

143014 Two soap bubbles each with radius $r_{1}$ and $r_{2}$ coalesce in vacuum under isothermal conditions to form a bigger bubble of radius $R$. then, $R$ is equal to

1 $\sqrt{r_{1}^{2}+r_{2}^{2}}$
2 $\sqrt{r_{1}^{2}-r_{2}^{2}}$
3 $\mathrm{r}_{1}+\mathrm{r}_{2}$
4 $\frac{\sqrt{\mathrm{r}_{1}^{2}+\mathrm{r}_{2}^{2}}}{2}$
5 $2 \sqrt{r_{1}^{2}+r_{2}^{2}}$
CGPET 2005
Mechanical Properties of Fluids

143015 A ball of radius $r$ and density $\rho$ falls freely under gravity through a distance $h$ before entering water. Velocity of ball does not change even on entering water. If viscosity of water is $\eta$ the value of $h$ is given by

1 $\frac{2}{9} r^{2}\left(\frac{1-\rho}{\eta}\right) g$
2 $\frac{2}{81} r^{2}\left(\frac{\rho-1}{\eta}\right) g$
3 $\frac{2}{81} r^{4}\left(\frac{\rho-1}{\eta}\right)^{2} g$
4 $\frac{2}{9} r^{4}\left(\frac{\rho-1}{\eta}\right)^{2} g$
AIIMS-27.05.2018(M)
Mechanical Properties of Fluids

143016 A spherical solid ball of volume $V$ is made of a material of density $\rho_{1}$. It is falling through a liquid of density $\rho_{1}\left(\rho_{2} \lt \rho_{1}\right)$. Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed $v$, i.e., $F_{\text {viscous }}=-\mathbf{k v}_{\mathbf{t}}{ }^{2}(k>0)$. The terminal speed of the ball is

1 $\sqrt{\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}}$
2 $\frac{\mathrm{Vg} \rho_{1}}{\mathrm{k}}$
3 $\sqrt{\frac{\operatorname{Vg} \rho_{1}}{\mathrm{k}}}$
4 $\frac{\operatorname{Vg}\left(\rho_{1}-\rho_{2}\right)}{\mathrm{k}}$
AIIMS-2013
Mechanical Properties of Fluids

143017 If the terminal speed of a sphere of gold (density $=19.5 \mathrm{~kg} / \mathrm{m}^{3}$ ) is $0.2 \mathrm{~m} / \mathrm{s}$ in a viscous liquid (density $=1.5 \mathrm{~kg} / \mathrm{m}^{3}$ ), find the terminal speed of a sphere of silver (density $=10.5$ $\mathrm{kg} / \mathrm{m}^{3}$ ) of the same size in the same liquid.

1 $0.4 \mathrm{~m} / \mathrm{s}$
2 $0.133 \mathrm{~m} / \mathrm{s}$
3 $0.1 \mathrm{~m} / \mathrm{s}$
4 $0.2 \mathrm{~m} / \mathrm{s}$
AIIMS-2008