Calculating Friction Using Coeffcients

Q. Find the ratio of tension $T_1$ and $T_2$ in the string as shown in figure if the whole system is moving with constant acceleration of $4m/s^2$ under the influence of force of magnitude $220N$ acting on block of mass $15kg$ . Assume the coefficient of friction to be $\mu =1/3$ and $g=10m/s^2$.

1. $0.35$
2. $0.45$
3. $0.2$
4. $5$

Q. There is a chain of length $6\text{m}$ and coefficient of friction $\frac{1}{2}$. What will be the maximum length of chain which can be held outside the table without sliding?

1. $2\text{m}$
2. $4\text{m}$
3. $3\text{m}$
4. $1\text{m}$

Q. A coefficient of friction more than unity means that the friction is stronger than normal force.

1. False
2. True

Q.

Two blocks of masses $m_1=4kg$ and $m_2=6kg$ are connected by a string of negligible mass passing over a frictionless pulley as shown in the figure. The coefficient of friction between block $m_1$ and the horizontal surface is 0.4. When the system is released, the masses $m_{1}and{m}_2$ start accelerating. What additional mass $m$ should be placed over mass $m_1$ so that the masses $(m_1+m)$ slide with a uniform speed?

1. 9 kg

2. 10 kg

3. 11 kg

4. 12 kg

Q. Figure 5.18 shows a man standing stationary with respect to a horizontal conveyor belt that is accelerating with 1 m s-2. What is the net force on the man? If the coefficient of static friction between the man’s shoes and the belt is 0.2, up to what acceleration of the belt can the man continue to be stationary relative to the belt ? (Mass of the man = 65 kg.)

Q. In the figure shown, find the tension in the string connecting the two bodies.

1. $20\text{N}$
2. $30\text{N}$
3. $10\text{N}$
4. Zero

Q. The maximum speed of a car on a road turn of radius $30m$, if the coefficient of friction between the tyres and the road is $0.4$, will be

1. $9.84m/s$
2. $10.84m/s$
3. $7.84m/s$
4. $5.84m/s$

Q. A disc revolves with a speed of 33 (1/3)rev/min, and has a radius of 15 cm. Two coins are placed at 4 cm and 14 cm away from the centre of the record. If the co-efficient of friction between the coins and the record is 0.15, which of the coins will revolve with the record ?

Q. Two blocks of mass $m_1$ and $m_2$ are connected by a weightless rod on a plane having inclination of ${37}^{\circ }$. The coefficients of dynamic friction of $m_1$ and $m_2$ with the inclined plane are $\mu =0.25$. Then the common acceleration of the two blocks and the tension in the rod are

1. $4{\text{m/s}}^2,T=0$
2. $2{\text{m/s}}^2,T=5\text{N}$
3. $10{\text{m/s}}^2,T=10\text{N}$
4. $15{\text{m/s}}^2,T=9\text{N}$

Q. Starting from rest, a body slides down a ${45}^{\circ }$ rough inclined plane in twice the time it takes to slide down the same distance in the absence of friction (with same inclination). The coefficient of friction between the body and the inclined plane is

1. $0.33$
2. $0.75$
3. $0.80$
4. $0.25$

Q. Block A of mass $m$ and block $B$ of mass $2m$ are placed on a fixed tringular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure . The wedge is inclined at ${45}^{\circ }$ to the horizointal on both sides. If the coefficient of friction between the block $A$ and the wedge is $\frac{2}{3}$ and that between block B and the wedge is $\frac{1}{3}$ and both the blocks $A$ and $B$ are released from rest, the acceleration of $A$ will be

1. $-1m/s^2$
2. $1.2m/s^2$
3. $0.2m/s^2$
4. $\text{zero}$

Q. A block of mass $m$ is placed on another block of mass $M$ which itself is lying on a horizontal surface. The coefficient of friction between two blocks is ${\mu }_1$ and that between the block of mass $M$ and horizontal surface is ${\mu }_2$. What maximum horizontal force can be applied to the lower block so that the two blocks move without separation?

1. $(M+m)({\mu }_2-{\mu }_1)g$
2. $(M-m)({\mu }_2-{\mu }_1)g$
3. $(M-m)({\mu }_2+{\mu }_1)g$
4. $(M+m)({\mu }_2+{\mu }_1)g$

Q.

A shell of mass m at rest explodes in two parts with mass ratio 1:2. The surface has friction coefficient $\mu$. What is the ratio of stopping distance

1. 4/1

2. 3/2

3. 3/1

4. 2/1

Q. The upper half of an inclined plane of inclination $\theta$ is perfectly smooth while lower half is rough. A block starting from rest at the top of the plane will again come to rest at the bottom. If the coefficient of friction between the block and lower half of plane is given by

1. $2\tan \theta$
2. $\tan \theta$
3. $2\cot \theta$
4. $2\cos \theta$

Q.

A boy of mass m is sliding down a vertical pole by pressing it with a horizontal force $f$. If $\mu$ is the coefficient of friction between his palms and the pole, the acceleration with which he slides down will be equal to

1. $g$

2. $\frac{\mu f}{m}$

3. $g+\frac{\mu f}{m}$

4. $g-\frac{\mu f}{m}$

Q.

A trolley of mass M is attached to a block of mass m by a string passing over a frictionless pulley as shown in the figure. If the coefficient of friction between the trolley and the surface below is $\mu ,$ what is the acceleration of the trolley and the block system when they are released?

1. $\left(\frac{m-M}{m+M}\right)g$

2. $\frac{m}{M}g$

3. $\left(\frac{\mu m-M}{m+M}\right)g$

4. $\left(\frac{m-\mu M}{m+M}\right)g$

Q. A heavy uniform chain lies on a horizontal table top. If the coefficient of friction between the chain and the table surface is $0.25$, then the maximum fraction of length of chain that can overhang on the edge of the table is

1. $0.20$
2. $0.35$
3. $0.25$
4. $0.15$

Q. Block A of mass $m$ and block $B$ of mass $2m$ are placed on a fixed tringular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure . The wedge is inclined at ${45}^{\circ }$ to the horizointal on both sides. If the coefficient of friction between the block $A$ and the wedge is $\frac{2}{3}$ and that between block B and the wedge is $\frac{1}{3}$ and both the blocks $A$ and $B$ are released from rest, the acceleration of $A$ will be

1. $-1m/s^2$
2. $1.2m/s^2$
3. $0.2m/s^2$
4. $\text{zero}$

Q. Horizontal force needed to just move 10N box kept on horizontal surface(coefficient of static friction=0.2) is

1. 10 N
2. 20 N
3. 2 N
4. 1 N

Q. In the figure shown, the coefficient of static friction between $B$ and the wall is $\frac{2}{3}$ and the coefficient of kinetic friction between $B$ and the wall is $\frac{1}{3}$. Other contacts are smooth. If the minimum force ${}^{\prime }{F}^{\prime }$ required to lift $B$ up is $\frac{xmg}{2}$, then find $x$. Mass of $A$ is $2m$ and the mass of $B$ is $m$. Take $\tan \theta =\frac{3}{4}$.

Q. A rought vertical board has an acceleration $a$, so that a $2\text{kg}$ block pressing against it does not fall. The coefficient of friction between the block and the board is $\mu$, then

1. $\mu >\frac{a}{g}$
2. $\mu <\frac{g}{a}$
3. $\mu <\frac{a}{g}$
4. $\mu >\frac{g}{a}$

Q.

Two blocks A and B are connected to each other by a string and a spring of force constant k, as shown in the figure. The string passes over a frictionless pulley. Block B slides over the horizontal top surface of a stationary block C and block A slides along the vertical side of C both with the same uniform speed. If the coefficient of friction between the surfaces of the blocks is $\mu$ and the mass of block A is m, what is the mass of block B?

1. $\frac{m}{\sqrt{\mu }}$

2. $\frac{m}{\mu }$

3. $\sqrt{\mu m}$

4. $\mu m$

Q. A plank of mass $2\text{kg}$ and length $9\text{m}$ is placed on a horizontal floor. A small block of mass $1\text{kg}$ is placed on top of the plank at its right extreme end. The coefficient of friction between the plank and the floor is $0.5$ and that between the plank and the block is $0.2$. If a horizontal force of $30\text{N}$ starts acting on the plank to the right, the time after which the block will fall off the plank is
(Take $g=10{\text{ms}}^{-2}$)

1. $2.96\text{s}$
2. $2\text{s}$
3. $1.75\text{s}$
4. $3.14\text{s}$

Q. Find the least pulling force acting at an angle of ${30}^{\circ }$ with the horizontal, which can just slide a body of mass $10\text{kg}$ along a rough horizontal surface $[{\mu }_s={\mu }_k=\frac{1}{\sqrt{3}},g=10m/s^2]$

1. $25\text{N}$
2. $75\text{N}$
3. $50\text{N}$
4. $100\text{N}$

Q.

The block $m_1$ is loaded on the block $m_2$. If there is no relative sliding between the blocks and the inclined plane is smooth, find the friction force between the blocks.

1. $m_{1}gsin\theta$

2. ($m_1+m_2$)g sin$\theta$

3. 0

4. $\mu m_{1}gcos\theta$

Q. If circular race track is banked at angle $\theta$ ($\theta >$ angle of repose), radius of track is $r$ and $\mu$ is coefficient of friction between car and road. Calculate minimum speed on car on inclined plane to avoid slipping?

1. $v=\left[rg\left(\frac{\tan \theta -\mu }{1+\mu \tan \theta }\right)\right]$
2. $v={\left[rg\left(\frac{\tan \theta +\mu }{1-\mu \tan \theta }\right)\right]}^{1/2}$
3. $v={\left[rg\left(\frac{\tan \theta +\mu }{1+\mu \tan \theta }\right)\right]}^{1/2}$
4. $v={\left[rg\left(\frac{\tan \theta -\mu }{1+\mu \tan \theta }\right)\right]}^{1/2}$

Q. A motor cyclist rides around the well with a round vertical wall and does not fall down while riding because:

1. the force of gravity disappears
2. he loses weight some how
3. he is kept in this path due to the force exerted by surrounding air
4. the frictional force of the wall balances his weight

Q. If the pulley is pulled down with a force of $120\text{N}$ as shown in figure. The acceleration of $8\text{kg}$ block would be:
(All pulleys are light and frictionless, string is massless and inextensible)
(Take $g=10{\text{m/s}}^2$)

1. $0$
2. $5{\text{m/s}}^2$
3. $10{\text{m/s}}^2$
4. $4{\text{m/s}}^2$