Limiting Friction

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

Q. A particle of mass $m$ rests on a horizontal floor which has coefficient of static friction $\mu$. For the block to just move

1. a minimum force $F_{min}=\frac{\mu mg}{\sqrt{1+{\mu }^2}}$ has to be applied at an angle $\theta ={\tan }^{-1}\left(\frac{1}{\mu }\right)$ with the horizontal.
2. a minimum force $F_{min}=\mu mg$ has to be applied at an angle $\theta ={\tan }^{-1}\left(\mu \right)$ with the horizontal.
3. a minimum force $F_{min}=\frac{\mu mg}{\sqrt{1+{\mu }^2}}$ has to be applied at an angle $\theta ={\tan }^{-1}\left(\mu \right)$ with the horizontal.
4. a minimum force $F_{min}=\mu mg$ has to be applied at an angle $\theta ={\tan }^{-1}\left(\frac{1}{\mu }\right)$ with the horizontal.

Q. A body of mass $m=10\text{kg}$ is attached to one end of a wire, of length $0.3\text{m}$. The maximum angular speed $\left({\text{in rad s}}^{-1}\right)$, with which it can be rotated about its other end, in a space station is $(\text{Breaking stress of wire}=4.8\times {10}^7{\text{Nm}}^{-2},\text{and area of cross-section of the wire}={10}^{-2}{\text{cm}}^2)$, is .

Q. A block of mass $4\text{kg}$ is kept on a rough horizontal surface. The coefficient of static friction is $0.8$. If a force of $19\text{N}$ is applied on the block parallel to the floor, then the force of friction between the block and the floor is

1. $32\text{N}$
2. $18\text{N}$
3. $19\text{N}$
4. $9.8\text{N}$

Q. Identify the correct statement.

1. Static friction depends on the area of contact.
2. Kinetic friction depends on the area of contact.
3. Coefficient of static friction does not depend on the surfaces in contact.
4. Coefficient of kinetic friction is less than the coefficient of static friction.

Q. The minimum force required to start pushing a body up a rough (frictional coefficient $\mu$) inclined plane is$F_1$ while the minimum force needed to prevent it from sliding down is $F_2$. If the inclined plane makes an angle $\theta$ from the horizontal such that tan $\theta =2\mu$, then the ratio $\frac{F_1}{F_2}$is

Q.

What are the factors on which coefficient of friction depends?

Q.

A long horizontal rod has a bead which can slide along its length, and initially placed at a distance $L$ from one end $A$ of the rod. The rod is set in angular motion about $A$ with constant angular acceleration $a$. If the coefficient of friction between the rod and the bead is $m$, and gravity is neglected, then the time after which the bead starts slipping is

1. 

2. 

3. 

4. 

Q. A horizontal force of $10N$ is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is $0.2$. The weight of the block is

1. $2N$
2. $20N$
3. $100N$
4. $50N$

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. In a projectile motion, why does the vertical component of velocity become zero at the maximum height?

Q. A block of mass $m$ is dropped onto a spring of spring constant $k$ from a height $h$. The second end of the spring is attached to a second block of mass $M$ as shown in figure. Find the minimum value of $h$ so that the block $M$ bounces off the ground, if the block of mass $m$ sticks to the spring immediately after it comes into contact with it.

1. $\frac{(M^2+2mM)g}{2kM}$
2. $\frac{2(M^2+2mM)g}{km}$
3. $\frac{2(M^2+2mM)g}{kM}$
4. $\frac{(M^2+2mM)g}{2km}$

Q.

Calculate the contact force acting on the mass m placed over the inclined plane of friction coefficient 0.5 as shown:

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. zero
3. $4N$
4. $6N$

Q. three blocks A B and c of masses 4 kg, 2kg and 1kg are in contact with a frictionless force of 14 N is applied on the 4 kg block then the contact force between A and B is

Q. Assertion: On a rainy day it is difficult to drive a car or bus at high speed.
Reason: The value of coefficient of friction is lowered due to wetting of the surface.

1. Assertion is correct but Reason is incorrect
2. Both Assertion and Reason are correct but Reasion is not the correct explanation for Assertion
3. Both Assertion and Reason are correct and Reasion is the correct explanation for Assertion
4. Both Assertion and Reason are incorrect

Q. A block of mass $2\text{kg}$ is attached to a spring of force constant $k=10\text{N/m}$ as shown in the figure. Find the range in which the block can be kept without slipping when the block is pulled or pushed towards the spring (spring is elongated or compressed). Take $g=10{\text{m/s}}^2$.

1. $3.2\text{m}$
2. $1.6\text{m}$
3. $2.4\text{m}$
4. $4.8\text{m}$

Q. A wedge of mass $M$ fitted with a spring of spring constant $k$ is kept on a smooth horizontal surface. A rod of mass $m$ is kept on the wedge as shown in figure. The system is in equilibrium and at rest. Assuming that all surfaces are smooth, the potential energy stored in the spring is.

1. $\frac{2m^2{g}^2\tan \theta }{k}$
2. $\frac{m^2{g}^2\tan \theta }{k}$
3. $\frac{m^2{g}^2\tan \theta }{2k}$
4. $\frac{m^2{g}^2{\tan }^2\theta }{2k}$

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 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 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. Two blocks of masses 10 kg and 20 kg are connected by a massless string and are placed on a smooth horizontal surface as shown in the figure. If a force F = 600 N is applied to 10 kg block, then the tension in the string is:

1. 300 N
2. 400 N
3. 100 N
4. 200 N

Q.

The coefficient of static friction is 0.800 between the
soles of a sprinter’s running shoes and the level track
surface on which she is running. Determine the maxi-
mum acceleration she can achieve. Do you need to
know that her mass is 60.0 kg?

Q. A block of mass $4\text{kg}$ is kept on ground. The co-efficient of friction between the block and the ground is $0.8$. An external force of magnitude $30\text{N}$ is applied parallel to the ground. The resultant force exerted by the ground on the block is
(Take $g=10{\text{m/s}}^2$)

1. $40\text{N}$
2. $30\text{N}$
3. $60\text{N}$
4. $50\text{N}$

Q. The value of frictional force and acceleration of block of mass $10kg$ in the figure are
(Take $g=10{\text{m/s}}^2$)

1. $10N,1m/s^2$
2. $20N,2m/s^2$
3. $10N,0m/s^2$
4. $20N,0m/s^2$

Q. A uniform iron rod of length $L$ and radius $r$ is suspended from the ceiling by one of its end . What will be the elastic potential energy stored in the rod due to its own weight , given ${\rho }^2{g}^2{L}^{3}A=12Y$ where $\rho$ and Y are the density and young's modulus of the iron rod respectively ? $[A=\pi r^2]$

Q. A force $F$ is applied on a block 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.

Read the given statements and select the correct option.

Assertion: Friction is a self-adjusting force.

Reason: Friction does not depend upon the mass of the body.

1. If both assertion and reason are true and reason is a true explanation of assertion.

2. If both assertion and reason are true but reason is not the correct explanation of assertion.

3. If assertion is true but reason is false.

4. If both assertion and reason are false.

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. 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. $162kg$