05. Archimedes Principle
Mechanical Properties of Fluids

143184 A tank is filled with water of density $1 \mathrm{~g}$ per $\mathrm{cm}^{3}$ and oil of density $0.9 \mathrm{~g}$ per $\mathrm{cm}^{3}$. The height of water layer is $100 \mathrm{~cm}$ and of the oil layer is $400 \mathrm{~cm}$. If $\mathrm{g}=980 \mathrm{~cm} / \mathrm{s}^{2}$, then the velocity of efflux from an opening in the bottom of the tank is:

1 $\sqrt{900 \times 980} \mathrm{~cm} / \mathrm{s}$
2 $\sqrt{1000 \times 980} \mathrm{~cm} / \mathrm{s}$
3 $\sqrt{920 \times 980} \mathrm{~cm} / \mathrm{s}$
4 $\sqrt{950 \times 980} \mathrm{~cm} / \mathrm{s}$
Mechanical Properties of Fluids

143185 A water tank, open to the atmosphere, has a leak in it form of a circular hole, located at a height $h$ below the open surface of water. The velocity of the water coming out of the hole is:

1 $\sqrt{\mathrm{gh} / 2}$
2 $\sqrt{\mathrm{gh}}$
3 $\sqrt{2 \mathrm{gh}}$
4 $2 \sqrt{\mathrm{gh}}$
Mechanical Properties of Fluids

143187 A sphere of radius $R$ has a concentric spherical cavity of radius $r$. The relative density of the material of the sphere is $\sigma$. It just floats when placed in tank full of water.
The value of $\frac{R}{r}$ is

1 $\left(\frac{\sigma}{\sigma-1}\right)^{1 / 3}$
2 $\left(\frac{\sigma-1}{\sigma}\right)^{1 / 3}$
3 $\left(\frac{\sigma}{\sigma-1}\right)^{1 / 2}$
4 $\left(\frac{\sigma-1}{\sigma}\right)^{1 / 2}$
Mechanical Properties of Fluids

143188 The densities of wood and benzene at $0^{\circ} \mathrm{C}$ are $880 \mathrm{kgm}^{-3}$ and $900 \mathrm{kgm}^{-3}$, respectively. The coefficient of volume expansion is $1.2 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$ for wood and $1.5 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$ for benzene. Then the temperature at which a piece of wood just sinks in benzene is

1 $88^{\circ} \mathrm{C}$
2 $90^{\circ} \mathrm{C}$
3 $83.3^{\circ} \mathrm{C}$
4 $90.3^{\circ} \mathrm{C}$
NEET Test Series from KOTA - 10 Papers In MS WORD WhatsApp Here
Mechanical Properties of Fluids

143184 A tank is filled with water of density $1 \mathrm{~g}$ per $\mathrm{cm}^{3}$ and oil of density $0.9 \mathrm{~g}$ per $\mathrm{cm}^{3}$. The height of water layer is $100 \mathrm{~cm}$ and of the oil layer is $400 \mathrm{~cm}$. If $\mathrm{g}=980 \mathrm{~cm} / \mathrm{s}^{2}$, then the velocity of efflux from an opening in the bottom of the tank is:

1 $\sqrt{900 \times 980} \mathrm{~cm} / \mathrm{s}$
2 $\sqrt{1000 \times 980} \mathrm{~cm} / \mathrm{s}$
3 $\sqrt{920 \times 980} \mathrm{~cm} / \mathrm{s}$
4 $\sqrt{950 \times 980} \mathrm{~cm} / \mathrm{s}$
Mechanical Properties of Fluids

143185 A water tank, open to the atmosphere, has a leak in it form of a circular hole, located at a height $h$ below the open surface of water. The velocity of the water coming out of the hole is:

1 $\sqrt{\mathrm{gh} / 2}$
2 $\sqrt{\mathrm{gh}}$
3 $\sqrt{2 \mathrm{gh}}$
4 $2 \sqrt{\mathrm{gh}}$
Mechanical Properties of Fluids

143187 A sphere of radius $R$ has a concentric spherical cavity of radius $r$. The relative density of the material of the sphere is $\sigma$. It just floats when placed in tank full of water.
The value of $\frac{R}{r}$ is

1 $\left(\frac{\sigma}{\sigma-1}\right)^{1 / 3}$
2 $\left(\frac{\sigma-1}{\sigma}\right)^{1 / 3}$
3 $\left(\frac{\sigma}{\sigma-1}\right)^{1 / 2}$
4 $\left(\frac{\sigma-1}{\sigma}\right)^{1 / 2}$
Mechanical Properties of Fluids

143188 The densities of wood and benzene at $0^{\circ} \mathrm{C}$ are $880 \mathrm{kgm}^{-3}$ and $900 \mathrm{kgm}^{-3}$, respectively. The coefficient of volume expansion is $1.2 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$ for wood and $1.5 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$ for benzene. Then the temperature at which a piece of wood just sinks in benzene is

1 $88^{\circ} \mathrm{C}$
2 $90^{\circ} \mathrm{C}$
3 $83.3^{\circ} \mathrm{C}$
4 $90.3^{\circ} \mathrm{C}$
Mechanical Properties of Fluids

143184 A tank is filled with water of density $1 \mathrm{~g}$ per $\mathrm{cm}^{3}$ and oil of density $0.9 \mathrm{~g}$ per $\mathrm{cm}^{3}$. The height of water layer is $100 \mathrm{~cm}$ and of the oil layer is $400 \mathrm{~cm}$. If $\mathrm{g}=980 \mathrm{~cm} / \mathrm{s}^{2}$, then the velocity of efflux from an opening in the bottom of the tank is:

1 $\sqrt{900 \times 980} \mathrm{~cm} / \mathrm{s}$
2 $\sqrt{1000 \times 980} \mathrm{~cm} / \mathrm{s}$
3 $\sqrt{920 \times 980} \mathrm{~cm} / \mathrm{s}$
4 $\sqrt{950 \times 980} \mathrm{~cm} / \mathrm{s}$
Mechanical Properties of Fluids

143185 A water tank, open to the atmosphere, has a leak in it form of a circular hole, located at a height $h$ below the open surface of water. The velocity of the water coming out of the hole is:

1 $\sqrt{\mathrm{gh} / 2}$
2 $\sqrt{\mathrm{gh}}$
3 $\sqrt{2 \mathrm{gh}}$
4 $2 \sqrt{\mathrm{gh}}$
Mechanical Properties of Fluids

143187 A sphere of radius $R$ has a concentric spherical cavity of radius $r$. The relative density of the material of the sphere is $\sigma$. It just floats when placed in tank full of water.
The value of $\frac{R}{r}$ is

1 $\left(\frac{\sigma}{\sigma-1}\right)^{1 / 3}$
2 $\left(\frac{\sigma-1}{\sigma}\right)^{1 / 3}$
3 $\left(\frac{\sigma}{\sigma-1}\right)^{1 / 2}$
4 $\left(\frac{\sigma-1}{\sigma}\right)^{1 / 2}$
Mechanical Properties of Fluids

143188 The densities of wood and benzene at $0^{\circ} \mathrm{C}$ are $880 \mathrm{kgm}^{-3}$ and $900 \mathrm{kgm}^{-3}$, respectively. The coefficient of volume expansion is $1.2 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$ for wood and $1.5 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$ for benzene. Then the temperature at which a piece of wood just sinks in benzene is

1 $88^{\circ} \mathrm{C}$
2 $90^{\circ} \mathrm{C}$
3 $83.3^{\circ} \mathrm{C}$
4 $90.3^{\circ} \mathrm{C}$
Mechanical Properties of Fluids

143184 A tank is filled with water of density $1 \mathrm{~g}$ per $\mathrm{cm}^{3}$ and oil of density $0.9 \mathrm{~g}$ per $\mathrm{cm}^{3}$. The height of water layer is $100 \mathrm{~cm}$ and of the oil layer is $400 \mathrm{~cm}$. If $\mathrm{g}=980 \mathrm{~cm} / \mathrm{s}^{2}$, then the velocity of efflux from an opening in the bottom of the tank is:

1 $\sqrt{900 \times 980} \mathrm{~cm} / \mathrm{s}$
2 $\sqrt{1000 \times 980} \mathrm{~cm} / \mathrm{s}$
3 $\sqrt{920 \times 980} \mathrm{~cm} / \mathrm{s}$
4 $\sqrt{950 \times 980} \mathrm{~cm} / \mathrm{s}$
Mechanical Properties of Fluids

143185 A water tank, open to the atmosphere, has a leak in it form of a circular hole, located at a height $h$ below the open surface of water. The velocity of the water coming out of the hole is:

1 $\sqrt{\mathrm{gh} / 2}$
2 $\sqrt{\mathrm{gh}}$
3 $\sqrt{2 \mathrm{gh}}$
4 $2 \sqrt{\mathrm{gh}}$
Mechanical Properties of Fluids

143187 A sphere of radius $R$ has a concentric spherical cavity of radius $r$. The relative density of the material of the sphere is $\sigma$. It just floats when placed in tank full of water.
The value of $\frac{R}{r}$ is

1 $\left(\frac{\sigma}{\sigma-1}\right)^{1 / 3}$
2 $\left(\frac{\sigma-1}{\sigma}\right)^{1 / 3}$
3 $\left(\frac{\sigma}{\sigma-1}\right)^{1 / 2}$
4 $\left(\frac{\sigma-1}{\sigma}\right)^{1 / 2}$
Mechanical Properties of Fluids

143188 The densities of wood and benzene at $0^{\circ} \mathrm{C}$ are $880 \mathrm{kgm}^{-3}$ and $900 \mathrm{kgm}^{-3}$, respectively. The coefficient of volume expansion is $1.2 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$ for wood and $1.5 \times 10^{-3}{ }^{\circ} \mathrm{C}^{-1}$ for benzene. Then the temperature at which a piece of wood just sinks in benzene is

1 $88^{\circ} \mathrm{C}$
2 $90^{\circ} \mathrm{C}$
3 $83.3^{\circ} \mathrm{C}$
4 $90.3^{\circ} \mathrm{C}$