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

143062 $n$ identical droplets are charged to $v$ volt each.
If they coalesce to form a single large drop, then its potential will be

1 $n^{2 / 3} \mathrm{v}$
2 $n^{1 / 3} \mathrm{v}$
3 $\mathrm{nv}$
4 $\mathrm{v} / \mathrm{n}$
MP PMT 2010
Mechanical Properties of Fluids

143063 Under isothermal conditions, two soap bubbles of radii a and $b$ coalesce to form a single bubble of radius $c$. If the external pressure is $P$, then surface tension of the bubble is

1 $\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}+\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
2 $\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}-\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
3 $\frac{\mathrm{P}\left(\mathrm{c}^{2}+\mathrm{a}^{2}-\mathrm{b}^{2}\right)}{4\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}$
4 $\frac{\mathrm{P}\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
WB JEE 2021
Mechanical Properties of Fluids

143064 A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation (T) of the liquid drop depends on radius ( $r$ ) of the drop, density $(\rho)$ and surface tension (s) of the liquid. Which among the following will be a possible expression for $T$ (where, $k$ is a dimensionless constant)?

1 $\mathrm{k} \sqrt{\frac{\rho r}{\mathrm{~s}}}$
2 $k \sqrt{\frac{\rho^{2} r}{s}}$
3 $\mathrm{k} \sqrt{\frac{\rho r^{3}}{\mathrm{~s}}}$
4 $\mathrm{k} \sqrt{\frac{\rho r^{3}}{\mathrm{~s}^{2}}}$
WB JEE 2018
Mechanical Properties of Fluids

143065 1000 droplets of water having $2 \mathrm{~mm}$ diameter each coalesce to form a single drop. Given the surface tension of water is $0.072 \mathrm{Nm}^{-1}$. The energy loss in the process is

1 $8.146 \times 10^{-4} \mathrm{~J}$
2 $4.4 \times 10^{-4} \mathrm{~J}$
3 $2.108 \times 10^{-5} \mathrm{~J}$
4 $4.7 \times 10^{-1} \mathrm{~J}$
WB JEE 2016
Mechanical Properties of Fluids

143066 A gas bubble of $\mathbf{2} \mathrm{cm}$ diameter rises through a liquid of density $1.75 \mathrm{~g} \mathrm{~cm}^{-3}$ with a fixed speed of $0.35 \mathrm{cms}^{-1}$. Neglect the density of the gas. The coefficient of viscosity of the liquid is

1 870 poise
2 1120 poise
3 982 poise
4 1089 poise
WB JEE 2016
Join With Us for More Updates
Mechanical Properties of Fluids

143062 $n$ identical droplets are charged to $v$ volt each.
If they coalesce to form a single large drop, then its potential will be

1 $n^{2 / 3} \mathrm{v}$
2 $n^{1 / 3} \mathrm{v}$
3 $\mathrm{nv}$
4 $\mathrm{v} / \mathrm{n}$
MP PMT 2010
Mechanical Properties of Fluids

143063 Under isothermal conditions, two soap bubbles of radii a and $b$ coalesce to form a single bubble of radius $c$. If the external pressure is $P$, then surface tension of the bubble is

1 $\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}+\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
2 $\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}-\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
3 $\frac{\mathrm{P}\left(\mathrm{c}^{2}+\mathrm{a}^{2}-\mathrm{b}^{2}\right)}{4\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}$
4 $\frac{\mathrm{P}\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
WB JEE 2021
Mechanical Properties of Fluids

143064 A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation (T) of the liquid drop depends on radius ( $r$ ) of the drop, density $(\rho)$ and surface tension (s) of the liquid. Which among the following will be a possible expression for $T$ (where, $k$ is a dimensionless constant)?

1 $\mathrm{k} \sqrt{\frac{\rho r}{\mathrm{~s}}}$
2 $k \sqrt{\frac{\rho^{2} r}{s}}$
3 $\mathrm{k} \sqrt{\frac{\rho r^{3}}{\mathrm{~s}}}$
4 $\mathrm{k} \sqrt{\frac{\rho r^{3}}{\mathrm{~s}^{2}}}$
WB JEE 2018
Mechanical Properties of Fluids

143065 1000 droplets of water having $2 \mathrm{~mm}$ diameter each coalesce to form a single drop. Given the surface tension of water is $0.072 \mathrm{Nm}^{-1}$. The energy loss in the process is

1 $8.146 \times 10^{-4} \mathrm{~J}$
2 $4.4 \times 10^{-4} \mathrm{~J}$
3 $2.108 \times 10^{-5} \mathrm{~J}$
4 $4.7 \times 10^{-1} \mathrm{~J}$
WB JEE 2016
Mechanical Properties of Fluids

143066 A gas bubble of $\mathbf{2} \mathrm{cm}$ diameter rises through a liquid of density $1.75 \mathrm{~g} \mathrm{~cm}^{-3}$ with a fixed speed of $0.35 \mathrm{cms}^{-1}$. Neglect the density of the gas. The coefficient of viscosity of the liquid is

1 870 poise
2 1120 poise
3 982 poise
4 1089 poise
WB JEE 2016
For More Updates join with Us
Mechanical Properties of Fluids

143062 $n$ identical droplets are charged to $v$ volt each.
If they coalesce to form a single large drop, then its potential will be

1 $n^{2 / 3} \mathrm{v}$
2 $n^{1 / 3} \mathrm{v}$
3 $\mathrm{nv}$
4 $\mathrm{v} / \mathrm{n}$
MP PMT 2010
Mechanical Properties of Fluids

143063 Under isothermal conditions, two soap bubbles of radii a and $b$ coalesce to form a single bubble of radius $c$. If the external pressure is $P$, then surface tension of the bubble is

1 $\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}+\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
2 $\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}-\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
3 $\frac{\mathrm{P}\left(\mathrm{c}^{2}+\mathrm{a}^{2}-\mathrm{b}^{2}\right)}{4\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}$
4 $\frac{\mathrm{P}\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
WB JEE 2021
Mechanical Properties of Fluids

143064 A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation (T) of the liquid drop depends on radius ( $r$ ) of the drop, density $(\rho)$ and surface tension (s) of the liquid. Which among the following will be a possible expression for $T$ (where, $k$ is a dimensionless constant)?

1 $\mathrm{k} \sqrt{\frac{\rho r}{\mathrm{~s}}}$
2 $k \sqrt{\frac{\rho^{2} r}{s}}$
3 $\mathrm{k} \sqrt{\frac{\rho r^{3}}{\mathrm{~s}}}$
4 $\mathrm{k} \sqrt{\frac{\rho r^{3}}{\mathrm{~s}^{2}}}$
WB JEE 2018
Mechanical Properties of Fluids

143065 1000 droplets of water having $2 \mathrm{~mm}$ diameter each coalesce to form a single drop. Given the surface tension of water is $0.072 \mathrm{Nm}^{-1}$. The energy loss in the process is

1 $8.146 \times 10^{-4} \mathrm{~J}$
2 $4.4 \times 10^{-4} \mathrm{~J}$
3 $2.108 \times 10^{-5} \mathrm{~J}$
4 $4.7 \times 10^{-1} \mathrm{~J}$
WB JEE 2016
Mechanical Properties of Fluids

143066 A gas bubble of $\mathbf{2} \mathrm{cm}$ diameter rises through a liquid of density $1.75 \mathrm{~g} \mathrm{~cm}^{-3}$ with a fixed speed of $0.35 \mathrm{cms}^{-1}$. Neglect the density of the gas. The coefficient of viscosity of the liquid is

1 870 poise
2 1120 poise
3 982 poise
4 1089 poise
WB JEE 2016
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Mechanical Properties of Fluids

143062 $n$ identical droplets are charged to $v$ volt each.
If they coalesce to form a single large drop, then its potential will be

1 $n^{2 / 3} \mathrm{v}$
2 $n^{1 / 3} \mathrm{v}$
3 $\mathrm{nv}$
4 $\mathrm{v} / \mathrm{n}$
MP PMT 2010
Mechanical Properties of Fluids

143063 Under isothermal conditions, two soap bubbles of radii a and $b$ coalesce to form a single bubble of radius $c$. If the external pressure is $P$, then surface tension of the bubble is

1 $\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}+\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
2 $\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}-\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
3 $\frac{\mathrm{P}\left(\mathrm{c}^{2}+\mathrm{a}^{2}-\mathrm{b}^{2}\right)}{4\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}$
4 $\frac{\mathrm{P}\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
WB JEE 2021
Mechanical Properties of Fluids

143064 A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation (T) of the liquid drop depends on radius ( $r$ ) of the drop, density $(\rho)$ and surface tension (s) of the liquid. Which among the following will be a possible expression for $T$ (where, $k$ is a dimensionless constant)?

1 $\mathrm{k} \sqrt{\frac{\rho r}{\mathrm{~s}}}$
2 $k \sqrt{\frac{\rho^{2} r}{s}}$
3 $\mathrm{k} \sqrt{\frac{\rho r^{3}}{\mathrm{~s}}}$
4 $\mathrm{k} \sqrt{\frac{\rho r^{3}}{\mathrm{~s}^{2}}}$
WB JEE 2018
Mechanical Properties of Fluids

143065 1000 droplets of water having $2 \mathrm{~mm}$ diameter each coalesce to form a single drop. Given the surface tension of water is $0.072 \mathrm{Nm}^{-1}$. The energy loss in the process is

1 $8.146 \times 10^{-4} \mathrm{~J}$
2 $4.4 \times 10^{-4} \mathrm{~J}$
3 $2.108 \times 10^{-5} \mathrm{~J}$
4 $4.7 \times 10^{-1} \mathrm{~J}$
WB JEE 2016
Mechanical Properties of Fluids

143066 A gas bubble of $\mathbf{2} \mathrm{cm}$ diameter rises through a liquid of density $1.75 \mathrm{~g} \mathrm{~cm}^{-3}$ with a fixed speed of $0.35 \mathrm{cms}^{-1}$. Neglect the density of the gas. The coefficient of viscosity of the liquid is

1 870 poise
2 1120 poise
3 982 poise
4 1089 poise
WB JEE 2016
Join With Us for More Updates
Mechanical Properties of Fluids

143062 $n$ identical droplets are charged to $v$ volt each.
If they coalesce to form a single large drop, then its potential will be

1 $n^{2 / 3} \mathrm{v}$
2 $n^{1 / 3} \mathrm{v}$
3 $\mathrm{nv}$
4 $\mathrm{v} / \mathrm{n}$
MP PMT 2010
Mechanical Properties of Fluids

143063 Under isothermal conditions, two soap bubbles of radii a and $b$ coalesce to form a single bubble of radius $c$. If the external pressure is $P$, then surface tension of the bubble is

1 $\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}+\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
2 $\frac{\mathrm{P}\left(\mathrm{c}^{3}-\mathrm{a}^{3}-\mathrm{b}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
3 $\frac{\mathrm{P}\left(\mathrm{c}^{2}+\mathrm{a}^{2}-\mathrm{b}^{2}\right)}{4\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}$
4 $\frac{\mathrm{P}\left(\mathrm{a}^{3}+\mathrm{b}^{3}-\mathrm{c}^{3}\right)}{4\left(\mathrm{a}^{2}+\mathrm{b}^{2}-\mathrm{c}^{2}\right)}$
WB JEE 2021
Mechanical Properties of Fluids

143064 A spherical liquid drop is placed on a horizontal plane. A small disturbance causes the volume of the drop to oscillate. The time period of oscillation (T) of the liquid drop depends on radius ( $r$ ) of the drop, density $(\rho)$ and surface tension (s) of the liquid. Which among the following will be a possible expression for $T$ (where, $k$ is a dimensionless constant)?

1 $\mathrm{k} \sqrt{\frac{\rho r}{\mathrm{~s}}}$
2 $k \sqrt{\frac{\rho^{2} r}{s}}$
3 $\mathrm{k} \sqrt{\frac{\rho r^{3}}{\mathrm{~s}}}$
4 $\mathrm{k} \sqrt{\frac{\rho r^{3}}{\mathrm{~s}^{2}}}$
WB JEE 2018
Mechanical Properties of Fluids

143065 1000 droplets of water having $2 \mathrm{~mm}$ diameter each coalesce to form a single drop. Given the surface tension of water is $0.072 \mathrm{Nm}^{-1}$. The energy loss in the process is

1 $8.146 \times 10^{-4} \mathrm{~J}$
2 $4.4 \times 10^{-4} \mathrm{~J}$
3 $2.108 \times 10^{-5} \mathrm{~J}$
4 $4.7 \times 10^{-1} \mathrm{~J}$
WB JEE 2016
Mechanical Properties of Fluids

143066 A gas bubble of $\mathbf{2} \mathrm{cm}$ diameter rises through a liquid of density $1.75 \mathrm{~g} \mathrm{~cm}^{-3}$ with a fixed speed of $0.35 \mathrm{cms}^{-1}$. Neglect the density of the gas. The coefficient of viscosity of the liquid is

1 870 poise
2 1120 poise
3 982 poise
4 1089 poise
WB JEE 2016