Kinetic Friction

Q. Give three methods to reduce friction.

Q.

Check the equation 1/2mvsquare=mgh is dimensionally correct or not

Q.

A smooth block is released at rest on a ${45}^{\circ }$ incline and then slides a distance d. The time taken by the block to slide equal distances on rough incline is n times as much to slide on smooth incline of same angle of inclination. Then the coefficient of friction is

1. ${\mu }_k=\sqrt{1-\frac{1}{n^2}}$

2. ${\mu }_s=\sqrt{1-\frac{1}{n^2}}$

3. ${\mu }_k=1-\frac{1}{n^2}$

4. ${\mu }_s=1-\frac{1}{n^2}$

Q. A block of mass $10kg$ is pulled at constant speed on a rough horizontal surface by a force of $19.6N$. The coefficient of friction is

1. $0.1$
2. $0.2$
3. $0.3$
4. $0.4$

Q. A block slides down an inclined plane of inclination ${30}^{\circ }$ with a constant acceleration $g/4$ .Coefficient of kinetic friction is given by $\frac{1}{N\sqrt{3}}$. Then, the value of $N$ is

Q.

DetetDete the maximum acceleration of the train in which a box is lying on its floor will remain stationary given that the coefficient of static friction between the box and the trains floor is 0.15

Take g = 10m/s2

Q. ntthe ratio of acceleration of blocks A placed on smooth incline with block B placed on rough incline is 2:1 . the coefficient of kinetic friction between block B and incline?n

Q. The rope shown in figure wound around a cylinder of mass $4\text{kg}$ and moment of inertia $0.02{\text{kg m}}^2$ about the cylinder axis. If the cylinder rolls without slipping on a frictionless floor, then the linear acceleration of its centre of mass is -

1. $7.6{\text{m/sec}}^2$
2. $10{\text{m/sec}}^2$
3. $6.7{\text{m/sec}}^2$
4. $4.7{\text{m/sec}}^2$

Q. A body falling freelynfromfa given height H Hits an inclined plane in its path at a height h. As a result of this impact the direction of the velocity of the body becomes horizontal. For what value of h/H, the body will take the maximum time to reach the ground.

Q. A block starts moving up an inclined plane of inclination $30{}^{\circ }$ with an initial velocity of $v_0$. It comes back to its initial position with velocity $\frac{v_0}{2}$. The value of the coefficient of kinetic friction between the block and the inclined plane is close to $\frac{I}{1000}$. The nearest integer to I is .

Q. Which of the following forces will never give resultant force of $2N$

1. $2N\text{and}2N$
2. $1N\text{and}1N$
3. $1N\text{and}3N$
4. $1N\text{and}4N$

Q.

Where will a body weigh more 1 km above the surface of the earth or 1 km below the surface of the earth?

Q. A vertical frictionless semicircular track of radius $1\text{m}$ is fixed on the edge of a movable trolley (figure). Initially the system is at rest and a mass $m$ is kept at the the top of the track. The trolley starts moving to the right with a uniform horizontal acceleration $a=\frac{2g}{9}$. The mass slides down the track, eventually losing contact with it and dropping on to the floor. Calculate the angle $\theta$ at which it loses contact with the trolley and the track.

1. ${30}^{\circ }$
2. ${37}^{\circ }$
3. ${53}^{\circ }$
4. ${60}^{\circ }$

Q. A light rigid rod AB of length $3l$ has a point mass $m$ at end A and a point mass $2m$ at end B. It is kept on a smooth horizontal surface. Point C is the center of mass of the system. Initially, the system is at rest. The mass $2m$ is suddenly given a velocity $v_0$ towards right. Then:
[Take Z axis to be perpendicular to the plane of the paper.]

​​​​​​

1. The minimum moment of inertia (about Z-axis), $I_{zz}$ of the system is $5m{l}^2$.
2. The magnitude of tension in the rod in the subsequent motion is $\frac{2m{v}_0^2}{9l}$.
3. The ratio of moment of inertia about Z - axis at points A and B, $\frac{(I_{zz}{)}_A}{(I_{zz}{)}_B}=2$
4. Point C remains stationary during subsequent motion.

Q. A box of mass $50\text{kg}$ is kept on horizontal floor. When it is pushed by a horizontal force $F,$ it moves with constant velocity. If it is pushed by a horizontal force $1.5F,$ it moves with constant acceleration of $0.1{\text{m/s}}^2$. Find the value of $F.$

1. $10\text{N}$
2. $15\text{N}$
3. $20\text{N}$
4. $25\text{N}$

Q. Figure shows two blocks in contact and sliding down the inclined surface of inclination ${30}^{\circ }$. Coefficient of friction between the block of mass $4\text{kg}$ and the inclined plane is ${\mu }_1=0.3$ and that between the block of mass $2\text{kg}$ and the inclined plane is ${\mu }_2=0.20$. Assume coefficients of static and kinetic friction to be equal. Find the acceleration of $2\text{kg}$ block. Take $g=10{\text{m/s}}^2$.

1. $\frac{15-4\sqrt{3}}{3}{\text{m/s}}^2$
2. $5-\sqrt{3}{\text{m/s}}^2$
3. $\sqrt{15}{\text{m/s}}^2$
4. $5{\text{m/s}}^2$

Q.

Find the accelerations $a_1,a_2,a_3$ of the three blocks shown in figure (6-E8) if a horizontal force of 10 N is applied on (a) 2 kg block, (b) 3 kg block (c) 7 kg Block. Take g = $10m/s^2$

Q. Two blocks $A$ and $B$ are as shown in figure. The minimum horizontal force $F$ applied on block $B$ for which slipping begins at $B$ and ground is,

Diagram

1. $140N$
2. $100N$
3. $120N$
4. $50N$

Q.

Find the acceleration of the block of mass M in the situation of figure (6-E10). The coefficient of friction between the two blocks is ${\mu }_1$ and that between the bigger block and the ground is ${\mu }_2$.

Q. Coefficient of kinetic friction between $3\text{kg}\text{and}2\text{kg}$ block is $0.25$. The horizontal table surface is smooth. Find the acceleration $($in ${\text{m/s}}^2)$ of block of mass $10\text{kg}$.

1. $6$
2. $8$
3. $2$
4. $4$

Q. Two masses $2m$ and $m$ are connected by an inextensible light string. The string is passing over a light frictionless pulley. The mass $2m$ is resting on a surface and mass $m$ is hanging in air as shown in Fig. A particle of mass $m$ strikes the mass $m$ from below in case (I) with a velocity $v_0$ and in case (II) strikes mass $m$ with a velocity $v_0$ from top and sticks to it in both cases. Then,

1. The conservation of linear momentum can be applied in both the cases just before and just after collision
2. The conservation of linear momentum can be applied in case I but cannot be applied in case II just before and just after collision
3. The ratio of velocities of mass $m$ just after collision in first and second cases is $\frac{1}{2}$
4. The ratio of velocities of mass $m$ just after collision in first and second case is 2.

Q.

A father and son pushed their car to bring it to the side of the road as it had stalled in the middle of the road. They experienced that although they had to push with all their might initially to move the car, the push required to keep the car rolling was smaller, once the car started rolling. Explain.

Q. For the given dimensions shown in figure, find critical value of coefficient of friction $\mu$.

1. ${\mu }_{cr}=2$
   
2. ${\mu }_{cr}=\frac{1}{2}$
3. ${\mu }_{cr}=\frac{3}{2}$
4. ${\mu }_{cr}=\frac{2}{3}$

Q. A small mass slides down an inclined plane of inclination $\theta$ with the horizontal. The coefficent of friction is $\mu ={\mu }_{o}x$ where the $x$ is the distance through which the mass slides down and ${\mu }_o$ is a positive constant. Then the distance covered by the mass before it stops is

1. $\frac{2}{{\mu }_o}\tan \theta$
2. $\frac{4}{{\mu }_o}\tan \theta$
3. $\frac{1}{2{\mu }_o}\tan \theta$
4. $\frac{1}{{\mu }_o}\tan \theta$

Q.

The friction coefficient between an athlete's shoes and the ground is 0.90. Suppose Superman wears these shoes and races for 50 m. There is not upper limit on his capacity of running at high speeds.

Find the minimum time that he will have to take in completing the 50 m starting from rest.

1. sec

2. 10 sec

3. 30 sec

4. There is no limit to superman's speed. 50 m he can do in the blink of an eye

Q. Why are mountain roads generally made winding upwards rather than going straight up?

Q.

The friction coefficient between the two blocks shown in figure (6-E9) is $\mu$ but the floor is smooth.
(a) What maximum horizontal force F can be applied without disturbing the equilibrium of the system?
(b) Suppose the horizontal force applied is double of that found in Part (a). Find the accelerations of the two masses.

Q. Two persons pull each other through a massless rope in $\text{‘tug of war’}$ game. Who will win?

1. $\text{one who pulls the rope with a greater force}$
2. $\text{one who applies more friction force (shear force) on ground}$
3. $\text{one who applies more normal force(compressive force) on ground}$
4. $\text{one whose weight is more}$

Q.

Solve the previous problem if the friction coefficient between the 2.0 kg block and the plane below it is 0.5 and the plane below the 4.0 kg block is frictionless.

Q. A block is projected with a velocity $20\text{m/s}$ up the incline plane of inclination angle ${60}^{\circ }$ and stops after $2\text{s}$. If $g=10{\text{m/s}}^2$, then the approximate value of coefficient of friction is

1. $1.3$
2. $0.83$
3. $0.27$
4. $0.38$