Limiting Friction

Q. If mass of $A=10kg$, coefficient of static friction ${\mu }_s=0.2$, coefficient of kinetic friction ${\mu }_k=0.2$ and the mass of $B\text{is}20kg$. Then find the acceleration of the masses.

1. $6m/s^2$
2. $7m/s^2$
3. $8m/s^2$
4. $9m/s^2$

Q. Find the minimum value of '$m$', for the sytem to be in equilibrium. Take $g=10m/s^2$.

1. $10kg$
2. $15kg$
3. $20kg$
4. $25kg$

Q. A block of mass $1\text{kg}$ is kept on an inclined accelerating conveyor belt. Acceleration of the belt is $1{\text{m/s}}^2$ as shown in figure. Minimum coefficient of static friction between the belt and block to prevent slipping of the block will be: [Take $g=10{\text{m/s}}^2$]

1. $0.4$
2. $0.3$
3. $0.2$
4. $0.69$

Q. A block is moving on an inclined plane making an angle of ${45}^{\circ }$ with the horizontal and the co-efficient of friction between the block and the inclined plane is $\mu$. If the force required to just push it up the inclined plane is $3$ times the force required to just prevent it from sliding down, then the value of $\mu$ is
[Take($g=10m/s^2$]

1. $\mu =0.3$
2. $\mu =0.5$
3. $\mu =0.75$
4. $\mu =0.85$

Q. A variable force $F$ is applied on a block such that $F\propto t$, at an angle $\theta$ with the horizontal as shown in figure. Given $({\mu }_s>{\mu }_k)$. Find the correct graph between frictional force and time. (where $t=$ time)

1. 
2. 
3. 
4. 

Q. In the figure, $m_A=2\text{kg}$ and $m_B=4\text{kg}$. The minimum value of $F$ for which $A$ starts slipping over $B$ is $(g=10{\text{ms}}^{-2})$

1. $24\text{N}$
2. $36\text{N}$
3. $12\text{N}$
4. $20\text{N}$

Q. A block of mass $10\text{kg}$ is at rest on a rough horizontal surface. A force of $40\text{N}$ is applied on it as shown in figure. The acceleration of the block is: (Take $g=10{\text{m/s}}^2$)

1. $0{\text{m/s}}^2$
2. $10{\text{m/s}}^2$
3. $20{\text{m/s}}^2$
4. $30{\text{m/s}}^2$

Q. A block of mass $4\text{kg}$ is kept on an inclined plane having an angle of inclination ${37}^{\circ }$ attached with a spring of force constant $20\text{N/m}$ as shown in the figure. If the coefficient of friction between the block and incline is $0.8$, find the range in which the block can be at rest without slipping from its equilibrium position?

1. $2.56\text{m}$
2. $5\text{m}$
3. $10\text{m}$
4. $1.25\text{m}$

Q. The figure shows a man standing stationary with respect to a horizontal conveyor belt. If the coefficient of static friction between the man's shoes and the belt is $0.2$, upto what acceleration of the belt can the man continue to be stationary relative to the belt? Mass of the man $=65\text{kg}$. ($g=10{\text{m/s}}^2$)

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

Q. A block of mass $2\text{kg}$ is placed on the floor. The coefficient of static friction is $0.4$. If a force of $2.8\text{N}$ is applied on the block parallel to the floor, the force of friction between the block and floor is (take $g=10{\text{ms}}^{-2}$)

1. $2.8\text{N}$
2. $8\text{N}$
3. $2\text{N}$
4. $\text{zero}$

Q. A block placed on a rough horizontal table is acted upon by an external horizontal force $P$. The graph of frictional force $F$ against external force $P$ is

1. 
2. 
3. 
4. 

Q. In a rotor, a hollow vertical cylindrical structure rotates about its axis and a person rests against the inner wall. At a particular speed of the rotor, the floor below the person is removed and the person hangs resting against the wall without any floor. If radius of rotor is $2m$ and ${\mu }_s=0.2$ what will be the minimum angular velocity at which floor may be removed :-

1. $2\text{rad/s}$
2. $5\text{rad/s}$
3. $10\text{rad/s}$
4. None of them

Q. A block is in contact with the inner wall of a hollow cylindrical drum as shown in figure. The minimum angular velocity (in $\text{rad/s}$) needed for the cylinder to keep the block stationary relative to itself, when the cylinder is vertical and rotating about its axis will be

Q. The maximum value of mass of block $C$ so that neither $A$ nor $B$ moves is (Given that mass of $A$ is $100kg$ and that of $B$ is $140kg$. Pulleys are smooth and friction coefficient between $A$ and $B$ and between $B$ and horizontal surface is :($\mu =0.3,g=10m/s^2$).

1. $210kg$
2. $190kg$
3. $185kg$
4. $162kg$

Q. Find the minimum value of coefficient of friction between the $4kg$ block and the surface for the system to be at rest for the figure shown.

1. $0.4$
2. $0.5$
3. $0.6$
4. $0.75$

Q. A long conveyor belt is designed to transport packages of various weights. Each $20kg$ package has a coefficient of kinetic friction $0.25$. If the speed of the conveyor belt is $10m/s$ and then it suddenly stops, the distance the package will slide before coming to rest is

1. $6\text{m}$
2. $10\text{m}$
3. $15\text{m}$
4. $20\text{m}$

Q. A block of mass $3kg$ is placed on the floor of coefficient of static friction is $0.4$. The force of $3.5N$ applied on the block. Calculate the force of friction and discuss the motion of the body.

1. $3.5N$, moves
2. $3.5N$, remains at rest
3. $11.76N$, moves
4. $11.76N$, remains at rest

Q. Two blocks of equal mass $2M$ are connected by a string and are kept on a rough horizontal surface as shown in the figure. $\mu$ is the coefficient of friction between the blocks and the surface. If $0<F_1-F_2<4\mu Mg$ , then choose the correct statement.

1. The direction of friction on block $A$ is towards right.
2. The direction of friction on block $B$ is either towards left or right
3. Tension in the string is zero
4. Friction force on block $B$ is zero

Q. A block of mass $4\text{kg}$ is placed on a rough horizontal plane. A time depedent force $F=k{t}^2$ acts on the block, where $k=2{\text{N/s}}^2$. Coefficient of static friction $\mu =0.8$. Force of friction between the block and the plane at $t=2\text{s}$ is

1. $8\text{N}$
2. $4\text{N}$
3. $2\text{N}$
4. $32\text{N}$

Q. A hockey player is moving northward and suddenly turns westward with the same speed to avoid an opponent. The force that acts on the player is

1. frictional force along westward
2. muscles force along southward
3. frictional force along south-west
4. muscle force along south-west

Q. A block placed on a rough horizontal table is acted upon by an external horizontal force $P$. The graph of frictional force $F$ against external force $P$ is

1. 
2. 
3. 
4. 

Q. Two blocks of equal mass $2M$ are connected by a string and are kept on a rough horizontal surface as shown in the figure. $\mu$ is the coefficient of friction between the blocks and the surface. If $0<F_1-F_2<4\mu Mg$ , then choose the correct statement.

1. The direction of friction on block $A$ is towards right.
2. The direction of friction on block $B$ is either towards left or right
3. Tension in the string is zero
4. Friction force on block $B$ is zero

Q. Two blocks of masses $2kg$ and $4kg$ are connected by a light string and kept on horizontal surface. A force of $16N$ is acted on 4kg block horizontally as shown in figure. Besides it is given that coefficient of friction between 4~kg and ground is 0.3 and between $2kg$ block and ground is 0.6. Then frictional force between $2kg$ block and ground is

1. $12N$
2. $4N$
3. $6N$
4. zero

Q. A wooden box of mass $8\text{kg}$ slides down an inclined plane of inclination ${30}^{\circ }$ to the horizontal with a constant acceleration of $0.4{\text{m/s}}^2$. What is the force of friction between the box and inclined plane? $(g=10{\text{m/s}}^2)$

1. $36.8\text{N}$
2. $76.8\text{N}$
3. $65.6\text{N}$
4. $\text{None of these}$

Q. A man who is freely falling is holding two blocks of equal mass as shown in the figure below. He shifts the location of the blocks as shown. What is the shift in the position of the man in x-direction?

1. Towards left
2. Towards right
3. No shift
4. Cannot say

Q. In the figure given below, two blocks of mass $m$ and $M$ are connected through a light inextensible rope. Then, find the tension in the connecting rope. Consider coefficient of static friction between the inclined surface and the blocks to be $\mu$.

1. $(M+m)g\sin \theta$
2. $(M+m)g\sin \theta -\mu mg\cos \theta$
3. $\text{Zero}$
4. $(M+m)g\cos \theta$

Q. A block placed on a horizontal surface is being pushed by a force F making an angle $\theta$ with the vertical. The coefficient of friction between block and surface is $\mu$. The force required to slide the block with uniform velocity on the floor is

1. $\frac{\mu mg}{(sin\theta -\mu cos\theta )}$
2. $\frac{(sin\theta -\mu cos\theta )}{\mu mg}$
3. $\mu mg$
4. $\text{None of these}$

Q. A mass $m$ rests on a horizontal surface. The coefficient of friction between the mass and the surface is $\mu$. If the mass is pulled by a force $F$ as shown in figure, the limiting friction between the mass and the surface will be

1. $\mu mg$
2. $\mu [mg-\left(\frac{\sqrt{3}}{2}F\right)]$
3. $\mu [mg-\left(\frac{F}{2}\right)]$
4. $\mu [mg+\left(\frac{F}{2}\right)]$

Q. A crate is on the flat surface of a truck of coefficient of static friction ${\mu }_s=0.8$ and coefficient of kinetic friction ${\mu }_k=0.7$. The coefficient of kinetic friction between the truck tires and the road surface is $0.9$. If the truck suddenly stops from an initial speed of $15m/s$ with maximum braking (wheels skidding), determine the displacement of the crate before it comes to rest.

1. $3.2m$
2. $2m$
3. $2.79m$
4. $1m$

Q. In the figure given below, two blocks of mass $m$ and $M$ are connected through a light inextensible rope. Then, find the tension in the connecting rope. Consider coefficient of static friction between the inclined surface and the blocks to be $\mu$.

1. $(M+m)g\sin \theta$
2. $(M+m)g\sin \theta -\mu mg\cos \theta$
3. $\text{Zero}$
4. $(M+m)g\cos \theta$