Friction

Q. A dimensionally consistent relation for the volume V of a liquid of coefficient of viscosity $\eta$ flowing per second through a tube of radius r and length l and having a pressure difference P across its end, is

1. V=$\frac{\pi P{\gamma }^4}{8\eta l}$
2. V=$\frac{\pi \eta l}{8P{\gamma }^4}$
3. V=$\frac{8P\eta l}{\pi {\gamma }^4}$
4. V = $\frac{\pi P\eta }{8l{\gamma }^4}$

Q. What will be the total resistance offered to the flow of water by the system of pipe $1$, pipe $2$, pipe $3$ and pipe ignoring the joints? If all the pipes are of length $3\text{m}$ and radius $2\text{m}$ and '$\eta$' is viscosity of water. (Assume $\pi =3$)

1. $1.25\eta$
2. $3\eta$
3. $4.5\eta$
4. $9\eta$

Q. The velocity profile of a fluid over a flat plate is parabolic in nature. At a distance of $15\text{cm}$ from the plate, the velocity of fluid is maximum i.e $100\text{cm/s}$. Calculate the shear stress at a distance of $10\text{cm}$ from the plate if the viscosity of the fluid is $10\text{poise}$.

1. $4.53{\text{N/m}}^2$
2. $2.26{\text{N/m}}^2$
3. $2.35{\text{N/m}}^2$
4. None of these

Q. The velocity profile of a fluid over a flat plate is parabolic in nature. At a distance of $15\text{cm}$ from the plate, the velocity of fluid is maximum i.e $100\text{cm/s}$. Calculate the shear stress at a distance of $10\text{cm}$ from the plate if the viscosity of the fluid is $10\text{poise}$.

1. $4.53{\text{N/m}}^2$
2. $2.26{\text{N/m}}^2$
3. $2.35{\text{N/m}}^2$
4. None of these

Q. By what factor will the flow rate of a viscous fluid through a pipe change, if the pipe radius is doubled, the fluid viscosity is doubled, the length is doubled and the pressure drop is reduced to a quarter of its previous value?

1. $4$
2. $16$
3. $\frac{1}{4}$
4. Doesn't change

Q. Which of the following correctly states how the viscosities of a liquid and a gas will change with temperature?

1. Viscosity increases with increase in temperature of a liquid and decreases with the increase in temperature of a gas
2. Viscosity increases with increase in temperature of a liquid and increases with the increase in temperature of a gas
3. Viscosity decreases with increase in temperature of a liquid and decreases with the increase in temperature of a gas
4. Viscosity decreases with increase in temperature of a liquid and increases with the increase in temperature of a gas

Q. When water $(\text{viscosity,}{\eta }_w=0.01\text{poise})$ and benzene $(\text{viscosity,}{\eta }_b=0.0065\text{poise})$ are allowed to flow through a pipe, it was found that the same amount of liquids are collected in the same time but the pressure drop that caused the flow are different. If the pressure drop in water is $0.015\text{atm}$, then the pressure drop in benzene will be

1. $2.3\times {10}^{-3}\text{atm}$
2. $975\times {10}^{-5}\text{atm}$
3. $4.33\times {10}^{-3}\text{atm}$
4. $2.3\times {10}^{-5}\text{atm}$

Q. A stationary uniform rod of mass $m=1\text{kg}$ and length $l=2\text{m}$ leans against a smooth vertical wall making an angle $\theta ={45}^o$ with rough horizontal floor. Find the frictional force that is exerted by the floor on the rod.

1. $5\text{N}$
2. $10\text{N}$
3. $20\text{N}$
4. $15\text{N}$

Q. A $50\text{kg}$ block slides down an incline with an angle of incline ${45}^{\circ }$. The coefficient of friction between the block and the incline is $0.3$. A worker applies a force on the block, so that it slides down the incline of length $2\text{m}$ with a constant velocity. What is the work done by the worker on the block?

1. $495.2\text{J}$
2. $-495.2\text{J}$
3. $-525.7\text{J}$
4. $525.7\text{J}$

Q. A cylinder initially kept at rest on a horizontal rough surface is given an angular velocity $10\text{rad/s}$. What is the distance travelled by the centre of mass of the cylinder till it begins pure rolling ?
Given: Coefficient of kinetic and static frcition are equal $(\mu =0.5)$ and radius of cylinder $R=3\text{m}$. Also, take $g=10{\text{m/s}}^2$.

1. $5\text{m}$
2. $10\text{m}$
3. $1\text{m}$
4. $20\text{m}$

Q. What will be the total resistance offered to the flow of water by the system of pipe $1$, pipe $2$, pipe $3$ and pipe ignoring the joints? If all the pipes are of length $3\text{m}$ and radius $2\text{m}$ and '$\eta$' is viscosity of water. (Assume $\pi =3$)

1. $1.25\eta$
2. $3\eta$
3. $4.5\eta$
4. $9\eta$

Q. Pipe $1$ has the radius and length of $0.2\text{m}$ and $50\text{m}$ respectively connected with the pipe $2$ having radius and length of $0.4\text{m}$ and $100\text{m}$ respectively. Find the total resistance offered to the flow of water by the system of pipes, Ignoring the resistance offered by the joint.
($\eta$ is the viscosity of water)

1. $8.95\times {10}^4\eta$
2. $5.5\times {10}^5\eta$
3. $4.56\times {10}^5\eta$
4. $2.86\times {10}^6\eta$

Q. A cylinder is given angular velocity ${\omega }_0$ and kept on a horizontal rough surface, the initial velocity is zero. Find out distance travelled by the cylinder before it performs pure rolling and work done by friction force.

1. $\frac{{\omega }_0^2}{12}\frac{R^2}{\mu g},-\frac{m{\omega }_0^2{R}^2}{18}$
2. $\frac{{\omega }_0^2}{18}\frac{R^2}{\mu g},\frac{m{\omega }_0^2{R}^2}{18}$
3. $\frac{{\omega }_0^2}{18}\frac{R^2}{\mu g},-\frac{m{\omega }_0^2{R}^2}{6}$
4. $\frac{{\omega }_0^2}{6}\frac{R^2}{\mu g},\frac{m{\omega }_0^2{R}^2}{6}$

Q. Pipe $1$ has the radius and length of $0.2\text{m}$ and $50\text{m}$ respectively connected with the pipe $2$ having radius and length of $0.4\text{m}$ and $100\text{m}$ respectively. Find the total resistance offered to the flow of water by the system of pipes, Ignoring the resistance offered by the joint.
($\eta$ is the viscosity of water)

1. $8.95\times {10}^4\eta$
2. $5.5\times {10}^5\eta$
3. $4.56\times {10}^5\eta$
4. $2.86\times {10}^6\eta$

Q. A hollow sphere is projected horizontally along a rough surface with speed $v$ and angular velocity ${\omega }_0$, find out the ratio $\left(\frac{v}{{\omega }_0}\right)$, so that the sphere stops moving after some time.

1. $R$
2. $\frac{4R}{3}$
3. $\frac{2R}{3}$
4. $\frac{7R}{3}$