08. Equation of Continuity
Mechanical Properties of Fluids

143369 An engine pumps out water continuously through a hose with a velocity $v$. If $m$ is the mass per unit length of the water jet, the rate at which the kinetic energy is imparted to water is

1 $\frac{1}{2} \mathrm{mv}^{2}$
2 $\frac{1}{2} \mathrm{mv}^{3}$
3 $\frac{1}{2} \mathrm{~m}^{2} \mathrm{v}^{2}$
4 $\mathrm{mv}^{3}$
5 $\frac{1}{4} \mathrm{mv}^{3}$
Mechanical Properties of Fluids

143370 Eight drops of a liquid of density $\rho$ and each of radius a are falling through air with a constant velocity $3.75 \mathrm{cms}^{-1}$. When the eight drops coalesce to form a single drop the terminal velocity of the new drop will be

1 $1.5 \times 10^{-2} \mathrm{~ms}^{-1}$
2 $2.4 \times 10^{-2} \mathrm{~ms}^{-1}$
3 $0.75 \times 10^{-2} \mathrm{~ms}^{-1}$
4 $25 \times 10^{-2} \mathrm{~ms}^{-1}$
5 $15 \times 10^{-2} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

143371 An incompressible non viscous fluid flows steadily through a cylindrical pipe which has radius $2 R$ at point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity of the fluid at point $A$ is $V$, its velocity at the point $B$ will be

1 $\mathrm{V} / 2$
2 $4 \mathrm{~V}$
3 $2 \mathrm{~V}$
4 $\mathrm{V}$
Mechanical Properties of Fluids

143372 A horizontal pipe of cross - sectional diameter 5 cm carries water at a velocity of $4 \mathrm{~m} / \mathrm{s}$. The pipe is connected to a smaller pipe with a crosssectional diameter $4 \mathrm{~cm}$. The velocity of water through the smaller pipe is :

1 $6.25 \mathrm{~m} / \mathrm{s}$
2 $5.0 \mathrm{~m} / \mathrm{s}$
3 $3.2 \mathrm{~m} / \mathrm{s}$
4 $2.56 \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143373 A rain drop of radius $r$ is falling through air starting from rest. The work done by all the forces on the drop, when it attains terminal velocity, is proportional to

1 $\mathrm{r}^{3}$
2 $r^{7}$
3 $r^{5}$
4 $r^{4}$
Mechanical Properties of Fluids

143369 An engine pumps out water continuously through a hose with a velocity $v$. If $m$ is the mass per unit length of the water jet, the rate at which the kinetic energy is imparted to water is

1 $\frac{1}{2} \mathrm{mv}^{2}$
2 $\frac{1}{2} \mathrm{mv}^{3}$
3 $\frac{1}{2} \mathrm{~m}^{2} \mathrm{v}^{2}$
4 $\mathrm{mv}^{3}$
5 $\frac{1}{4} \mathrm{mv}^{3}$
Mechanical Properties of Fluids

143370 Eight drops of a liquid of density $\rho$ and each of radius a are falling through air with a constant velocity $3.75 \mathrm{cms}^{-1}$. When the eight drops coalesce to form a single drop the terminal velocity of the new drop will be

1 $1.5 \times 10^{-2} \mathrm{~ms}^{-1}$
2 $2.4 \times 10^{-2} \mathrm{~ms}^{-1}$
3 $0.75 \times 10^{-2} \mathrm{~ms}^{-1}$
4 $25 \times 10^{-2} \mathrm{~ms}^{-1}$
5 $15 \times 10^{-2} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

143371 An incompressible non viscous fluid flows steadily through a cylindrical pipe which has radius $2 R$ at point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity of the fluid at point $A$ is $V$, its velocity at the point $B$ will be

1 $\mathrm{V} / 2$
2 $4 \mathrm{~V}$
3 $2 \mathrm{~V}$
4 $\mathrm{V}$
Mechanical Properties of Fluids

143372 A horizontal pipe of cross - sectional diameter 5 cm carries water at a velocity of $4 \mathrm{~m} / \mathrm{s}$. The pipe is connected to a smaller pipe with a crosssectional diameter $4 \mathrm{~cm}$. The velocity of water through the smaller pipe is :

1 $6.25 \mathrm{~m} / \mathrm{s}$
2 $5.0 \mathrm{~m} / \mathrm{s}$
3 $3.2 \mathrm{~m} / \mathrm{s}$
4 $2.56 \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143373 A rain drop of radius $r$ is falling through air starting from rest. The work done by all the forces on the drop, when it attains terminal velocity, is proportional to

1 $\mathrm{r}^{3}$
2 $r^{7}$
3 $r^{5}$
4 $r^{4}$
Mechanical Properties of Fluids

143369 An engine pumps out water continuously through a hose with a velocity $v$. If $m$ is the mass per unit length of the water jet, the rate at which the kinetic energy is imparted to water is

1 $\frac{1}{2} \mathrm{mv}^{2}$
2 $\frac{1}{2} \mathrm{mv}^{3}$
3 $\frac{1}{2} \mathrm{~m}^{2} \mathrm{v}^{2}$
4 $\mathrm{mv}^{3}$
5 $\frac{1}{4} \mathrm{mv}^{3}$
Mechanical Properties of Fluids

143370 Eight drops of a liquid of density $\rho$ and each of radius a are falling through air with a constant velocity $3.75 \mathrm{cms}^{-1}$. When the eight drops coalesce to form a single drop the terminal velocity of the new drop will be

1 $1.5 \times 10^{-2} \mathrm{~ms}^{-1}$
2 $2.4 \times 10^{-2} \mathrm{~ms}^{-1}$
3 $0.75 \times 10^{-2} \mathrm{~ms}^{-1}$
4 $25 \times 10^{-2} \mathrm{~ms}^{-1}$
5 $15 \times 10^{-2} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

143371 An incompressible non viscous fluid flows steadily through a cylindrical pipe which has radius $2 R$ at point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity of the fluid at point $A$ is $V$, its velocity at the point $B$ will be

1 $\mathrm{V} / 2$
2 $4 \mathrm{~V}$
3 $2 \mathrm{~V}$
4 $\mathrm{V}$
Mechanical Properties of Fluids

143372 A horizontal pipe of cross - sectional diameter 5 cm carries water at a velocity of $4 \mathrm{~m} / \mathrm{s}$. The pipe is connected to a smaller pipe with a crosssectional diameter $4 \mathrm{~cm}$. The velocity of water through the smaller pipe is :

1 $6.25 \mathrm{~m} / \mathrm{s}$
2 $5.0 \mathrm{~m} / \mathrm{s}$
3 $3.2 \mathrm{~m} / \mathrm{s}$
4 $2.56 \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143373 A rain drop of radius $r$ is falling through air starting from rest. The work done by all the forces on the drop, when it attains terminal velocity, is proportional to

1 $\mathrm{r}^{3}$
2 $r^{7}$
3 $r^{5}$
4 $r^{4}$
Mechanical Properties of Fluids

143369 An engine pumps out water continuously through a hose with a velocity $v$. If $m$ is the mass per unit length of the water jet, the rate at which the kinetic energy is imparted to water is

1 $\frac{1}{2} \mathrm{mv}^{2}$
2 $\frac{1}{2} \mathrm{mv}^{3}$
3 $\frac{1}{2} \mathrm{~m}^{2} \mathrm{v}^{2}$
4 $\mathrm{mv}^{3}$
5 $\frac{1}{4} \mathrm{mv}^{3}$
Mechanical Properties of Fluids

143370 Eight drops of a liquid of density $\rho$ and each of radius a are falling through air with a constant velocity $3.75 \mathrm{cms}^{-1}$. When the eight drops coalesce to form a single drop the terminal velocity of the new drop will be

1 $1.5 \times 10^{-2} \mathrm{~ms}^{-1}$
2 $2.4 \times 10^{-2} \mathrm{~ms}^{-1}$
3 $0.75 \times 10^{-2} \mathrm{~ms}^{-1}$
4 $25 \times 10^{-2} \mathrm{~ms}^{-1}$
5 $15 \times 10^{-2} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

143371 An incompressible non viscous fluid flows steadily through a cylindrical pipe which has radius $2 R$ at point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity of the fluid at point $A$ is $V$, its velocity at the point $B$ will be

1 $\mathrm{V} / 2$
2 $4 \mathrm{~V}$
3 $2 \mathrm{~V}$
4 $\mathrm{V}$
Mechanical Properties of Fluids

143372 A horizontal pipe of cross - sectional diameter 5 cm carries water at a velocity of $4 \mathrm{~m} / \mathrm{s}$. The pipe is connected to a smaller pipe with a crosssectional diameter $4 \mathrm{~cm}$. The velocity of water through the smaller pipe is :

1 $6.25 \mathrm{~m} / \mathrm{s}$
2 $5.0 \mathrm{~m} / \mathrm{s}$
3 $3.2 \mathrm{~m} / \mathrm{s}$
4 $2.56 \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143373 A rain drop of radius $r$ is falling through air starting from rest. The work done by all the forces on the drop, when it attains terminal velocity, is proportional to

1 $\mathrm{r}^{3}$
2 $r^{7}$
3 $r^{5}$
4 $r^{4}$
Mechanical Properties of Fluids

143369 An engine pumps out water continuously through a hose with a velocity $v$. If $m$ is the mass per unit length of the water jet, the rate at which the kinetic energy is imparted to water is

1 $\frac{1}{2} \mathrm{mv}^{2}$
2 $\frac{1}{2} \mathrm{mv}^{3}$
3 $\frac{1}{2} \mathrm{~m}^{2} \mathrm{v}^{2}$
4 $\mathrm{mv}^{3}$
5 $\frac{1}{4} \mathrm{mv}^{3}$
Mechanical Properties of Fluids

143370 Eight drops of a liquid of density $\rho$ and each of radius a are falling through air with a constant velocity $3.75 \mathrm{cms}^{-1}$. When the eight drops coalesce to form a single drop the terminal velocity of the new drop will be

1 $1.5 \times 10^{-2} \mathrm{~ms}^{-1}$
2 $2.4 \times 10^{-2} \mathrm{~ms}^{-1}$
3 $0.75 \times 10^{-2} \mathrm{~ms}^{-1}$
4 $25 \times 10^{-2} \mathrm{~ms}^{-1}$
5 $15 \times 10^{-2} \mathrm{~ms}^{-1}$
Mechanical Properties of Fluids

143371 An incompressible non viscous fluid flows steadily through a cylindrical pipe which has radius $2 R$ at point $A$ and radius $R$ at point $B$ farther along the flow direction. If the velocity of the fluid at point $A$ is $V$, its velocity at the point $B$ will be

1 $\mathrm{V} / 2$
2 $4 \mathrm{~V}$
3 $2 \mathrm{~V}$
4 $\mathrm{V}$
Mechanical Properties of Fluids

143372 A horizontal pipe of cross - sectional diameter 5 cm carries water at a velocity of $4 \mathrm{~m} / \mathrm{s}$. The pipe is connected to a smaller pipe with a crosssectional diameter $4 \mathrm{~cm}$. The velocity of water through the smaller pipe is :

1 $6.25 \mathrm{~m} / \mathrm{s}$
2 $5.0 \mathrm{~m} / \mathrm{s}$
3 $3.2 \mathrm{~m} / \mathrm{s}$
4 $2.56 \mathrm{~m} / \mathrm{s}$
Mechanical Properties of Fluids

143373 A rain drop of radius $r$ is falling through air starting from rest. The work done by all the forces on the drop, when it attains terminal velocity, is proportional to

1 $\mathrm{r}^{3}$
2 $r^{7}$
3 $r^{5}$
4 $r^{4}$