143313
Spherical ball of radius $(R)$ is falling in a viscous fluid of viscosity $\eta$ with a velocity (V). The retarding viscous force acting on the spherical ball is
1 directly proportional to radius (R) but inversely proportional to velocity (V)
2 directly proportional to both radius $(\mathrm{R})$ and to velocity (V)
3 inversely proportional to both radius (R) and velocity (V)
4 inversely proportional to radius (R) but directly proportional to velocity (V)
Explanation:
B From Stoke's law viscous force $\mathrm{F}=6 \pi \eta \mathrm{RV}$ $\mathrm{F} \propto \mathrm{R}$ $\mathrm{F} \propto \mathrm{V}$ So, force is directly proportional to both radius and velocity.
CG PET- 2006
Mechanical Properties of Fluids
143338
Water is flowing through a very narrow tube. The velocity of water below which the flow remains a streamline flow is known as
1 relative velocity
2 terminal velocity
3 critical velocity
4 particle velocity
Explanation:
C The velocity of water below which the flow remains streamline flow is knows as critical velocity. Critical velocity, $\mathrm{V}_{\mathrm{c}}=\frac{\mathrm{K \eta}}{\mathrm{r} \rho}$ Where, $\mathrm{K}=$ Reynold's number $\eta=\text { Coefficient of viscosity of liquid }$ $r=\text { Radius of capillary tube }$ $\rho=\text { Density of the liquid }$ SI unit of critical velocity is $\mathrm{m} / \mathrm{sec}$. Terminal velocity:- Terminal velocity is defined as the highest velocity attained by an object falling through a fluid. Relative velocity:- The relative velocity is defined as the velocity of an object with respect to another observer.
WB JEE 2012
Mechanical Properties of Fluids
143347
A body is floating partially immersed in a liquid. If the body and the liquid are taken to the moon the body will
1 continue to float exactly as in the earth
2 float with a larger part immersed in the liquid
3 float with a smaller part immersed in the liquid
4 $\operatorname{sink}$
Explanation:
A The mass of the object does not change by moving it to moon hence it does not depends it mass. The density of the fluid does not change when taken to the moon, then the volume displaced is unchanged. It means the body and the liquid are taken to the moon the body will continue to float exactly as in the earth.
WB JEE-2007
Mechanical Properties of Fluids
143358
A boat full of scrap iron is floating on water in lake. If all the iron is dropped into water, the water level of lake
1 go up
2 remain the same
3 rise very high
4 go very
Explanation:
B Law of floatation, Where, mass of liquid $=$ Volume of liquid $\times$ Density of liquid mass of solid $=$ Volume of solid $\times$ density of solid Let $\rho=$ Density of scrap iron $\mathrm{m}=$ mass of scrap iron $\therefore$ Volume of scrap iron $=\mathrm{m} / \rho$ $\therefore$ Reduction in immersed volume of boat $=\mathrm{m} / \rho$ Water-level of lake falls $=\mathrm{m} / \rho$ When scrap iron is dropped in level of lake rises $=\mathrm{m} / \rho$ By (ii) and (iii), water level remains the same. If all the iron is dropped into water, the water level of lake remain the same.
143313
Spherical ball of radius $(R)$ is falling in a viscous fluid of viscosity $\eta$ with a velocity (V). The retarding viscous force acting on the spherical ball is
1 directly proportional to radius (R) but inversely proportional to velocity (V)
2 directly proportional to both radius $(\mathrm{R})$ and to velocity (V)
3 inversely proportional to both radius (R) and velocity (V)
4 inversely proportional to radius (R) but directly proportional to velocity (V)
Explanation:
B From Stoke's law viscous force $\mathrm{F}=6 \pi \eta \mathrm{RV}$ $\mathrm{F} \propto \mathrm{R}$ $\mathrm{F} \propto \mathrm{V}$ So, force is directly proportional to both radius and velocity.
CG PET- 2006
Mechanical Properties of Fluids
143338
Water is flowing through a very narrow tube. The velocity of water below which the flow remains a streamline flow is known as
1 relative velocity
2 terminal velocity
3 critical velocity
4 particle velocity
Explanation:
C The velocity of water below which the flow remains streamline flow is knows as critical velocity. Critical velocity, $\mathrm{V}_{\mathrm{c}}=\frac{\mathrm{K \eta}}{\mathrm{r} \rho}$ Where, $\mathrm{K}=$ Reynold's number $\eta=\text { Coefficient of viscosity of liquid }$ $r=\text { Radius of capillary tube }$ $\rho=\text { Density of the liquid }$ SI unit of critical velocity is $\mathrm{m} / \mathrm{sec}$. Terminal velocity:- Terminal velocity is defined as the highest velocity attained by an object falling through a fluid. Relative velocity:- The relative velocity is defined as the velocity of an object with respect to another observer.
WB JEE 2012
Mechanical Properties of Fluids
143347
A body is floating partially immersed in a liquid. If the body and the liquid are taken to the moon the body will
1 continue to float exactly as in the earth
2 float with a larger part immersed in the liquid
3 float with a smaller part immersed in the liquid
4 $\operatorname{sink}$
Explanation:
A The mass of the object does not change by moving it to moon hence it does not depends it mass. The density of the fluid does not change when taken to the moon, then the volume displaced is unchanged. It means the body and the liquid are taken to the moon the body will continue to float exactly as in the earth.
WB JEE-2007
Mechanical Properties of Fluids
143358
A boat full of scrap iron is floating on water in lake. If all the iron is dropped into water, the water level of lake
1 go up
2 remain the same
3 rise very high
4 go very
Explanation:
B Law of floatation, Where, mass of liquid $=$ Volume of liquid $\times$ Density of liquid mass of solid $=$ Volume of solid $\times$ density of solid Let $\rho=$ Density of scrap iron $\mathrm{m}=$ mass of scrap iron $\therefore$ Volume of scrap iron $=\mathrm{m} / \rho$ $\therefore$ Reduction in immersed volume of boat $=\mathrm{m} / \rho$ Water-level of lake falls $=\mathrm{m} / \rho$ When scrap iron is dropped in level of lake rises $=\mathrm{m} / \rho$ By (ii) and (iii), water level remains the same. If all the iron is dropped into water, the water level of lake remain the same.
143313
Spherical ball of radius $(R)$ is falling in a viscous fluid of viscosity $\eta$ with a velocity (V). The retarding viscous force acting on the spherical ball is
1 directly proportional to radius (R) but inversely proportional to velocity (V)
2 directly proportional to both radius $(\mathrm{R})$ and to velocity (V)
3 inversely proportional to both radius (R) and velocity (V)
4 inversely proportional to radius (R) but directly proportional to velocity (V)
Explanation:
B From Stoke's law viscous force $\mathrm{F}=6 \pi \eta \mathrm{RV}$ $\mathrm{F} \propto \mathrm{R}$ $\mathrm{F} \propto \mathrm{V}$ So, force is directly proportional to both radius and velocity.
CG PET- 2006
Mechanical Properties of Fluids
143338
Water is flowing through a very narrow tube. The velocity of water below which the flow remains a streamline flow is known as
1 relative velocity
2 terminal velocity
3 critical velocity
4 particle velocity
Explanation:
C The velocity of water below which the flow remains streamline flow is knows as critical velocity. Critical velocity, $\mathrm{V}_{\mathrm{c}}=\frac{\mathrm{K \eta}}{\mathrm{r} \rho}$ Where, $\mathrm{K}=$ Reynold's number $\eta=\text { Coefficient of viscosity of liquid }$ $r=\text { Radius of capillary tube }$ $\rho=\text { Density of the liquid }$ SI unit of critical velocity is $\mathrm{m} / \mathrm{sec}$. Terminal velocity:- Terminal velocity is defined as the highest velocity attained by an object falling through a fluid. Relative velocity:- The relative velocity is defined as the velocity of an object with respect to another observer.
WB JEE 2012
Mechanical Properties of Fluids
143347
A body is floating partially immersed in a liquid. If the body and the liquid are taken to the moon the body will
1 continue to float exactly as in the earth
2 float with a larger part immersed in the liquid
3 float with a smaller part immersed in the liquid
4 $\operatorname{sink}$
Explanation:
A The mass of the object does not change by moving it to moon hence it does not depends it mass. The density of the fluid does not change when taken to the moon, then the volume displaced is unchanged. It means the body and the liquid are taken to the moon the body will continue to float exactly as in the earth.
WB JEE-2007
Mechanical Properties of Fluids
143358
A boat full of scrap iron is floating on water in lake. If all the iron is dropped into water, the water level of lake
1 go up
2 remain the same
3 rise very high
4 go very
Explanation:
B Law of floatation, Where, mass of liquid $=$ Volume of liquid $\times$ Density of liquid mass of solid $=$ Volume of solid $\times$ density of solid Let $\rho=$ Density of scrap iron $\mathrm{m}=$ mass of scrap iron $\therefore$ Volume of scrap iron $=\mathrm{m} / \rho$ $\therefore$ Reduction in immersed volume of boat $=\mathrm{m} / \rho$ Water-level of lake falls $=\mathrm{m} / \rho$ When scrap iron is dropped in level of lake rises $=\mathrm{m} / \rho$ By (ii) and (iii), water level remains the same. If all the iron is dropped into water, the water level of lake remain the same.
143313
Spherical ball of radius $(R)$ is falling in a viscous fluid of viscosity $\eta$ with a velocity (V). The retarding viscous force acting on the spherical ball is
1 directly proportional to radius (R) but inversely proportional to velocity (V)
2 directly proportional to both radius $(\mathrm{R})$ and to velocity (V)
3 inversely proportional to both radius (R) and velocity (V)
4 inversely proportional to radius (R) but directly proportional to velocity (V)
Explanation:
B From Stoke's law viscous force $\mathrm{F}=6 \pi \eta \mathrm{RV}$ $\mathrm{F} \propto \mathrm{R}$ $\mathrm{F} \propto \mathrm{V}$ So, force is directly proportional to both radius and velocity.
CG PET- 2006
Mechanical Properties of Fluids
143338
Water is flowing through a very narrow tube. The velocity of water below which the flow remains a streamline flow is known as
1 relative velocity
2 terminal velocity
3 critical velocity
4 particle velocity
Explanation:
C The velocity of water below which the flow remains streamline flow is knows as critical velocity. Critical velocity, $\mathrm{V}_{\mathrm{c}}=\frac{\mathrm{K \eta}}{\mathrm{r} \rho}$ Where, $\mathrm{K}=$ Reynold's number $\eta=\text { Coefficient of viscosity of liquid }$ $r=\text { Radius of capillary tube }$ $\rho=\text { Density of the liquid }$ SI unit of critical velocity is $\mathrm{m} / \mathrm{sec}$. Terminal velocity:- Terminal velocity is defined as the highest velocity attained by an object falling through a fluid. Relative velocity:- The relative velocity is defined as the velocity of an object with respect to another observer.
WB JEE 2012
Mechanical Properties of Fluids
143347
A body is floating partially immersed in a liquid. If the body and the liquid are taken to the moon the body will
1 continue to float exactly as in the earth
2 float with a larger part immersed in the liquid
3 float with a smaller part immersed in the liquid
4 $\operatorname{sink}$
Explanation:
A The mass of the object does not change by moving it to moon hence it does not depends it mass. The density of the fluid does not change when taken to the moon, then the volume displaced is unchanged. It means the body and the liquid are taken to the moon the body will continue to float exactly as in the earth.
WB JEE-2007
Mechanical Properties of Fluids
143358
A boat full of scrap iron is floating on water in lake. If all the iron is dropped into water, the water level of lake
1 go up
2 remain the same
3 rise very high
4 go very
Explanation:
B Law of floatation, Where, mass of liquid $=$ Volume of liquid $\times$ Density of liquid mass of solid $=$ Volume of solid $\times$ density of solid Let $\rho=$ Density of scrap iron $\mathrm{m}=$ mass of scrap iron $\therefore$ Volume of scrap iron $=\mathrm{m} / \rho$ $\therefore$ Reduction in immersed volume of boat $=\mathrm{m} / \rho$ Water-level of lake falls $=\mathrm{m} / \rho$ When scrap iron is dropped in level of lake rises $=\mathrm{m} / \rho$ By (ii) and (iii), water level remains the same. If all the iron is dropped into water, the water level of lake remain the same.
