JEE Friction PYQs with Video Solutions, Download PDF

A block of mass $$m$$ is placed on a surface having vertical cross section given by $$y = \frac{x^2}{4}$$. If coefficient of friction is 0.5, the maximum height above the ground at which block can be placed without slipping is:

An insect crawls up a hemispherical surface very slowly. The coefficient of friction between the insect and the surface is $$1/3$$. If the line joining the centre of the hemispherical surface to the insect makes an angle $$\alpha$$ with the vertical, the maximum possible value of $$\alpha$$ so that the insect does not slip is given by

A system of two blocks of masses $$m = 2$$ kg and $$M = 8$$ kg is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is $$0.5$$. The maximum horizontal force $$F$$ that can be applied to the block of mass $$M$$ so that the blocks move together will be $$(g = 9.8$$ m s$$^{-2})$$

A bag is gently dropped on a conveyor belt moving at a speed of $$2 \text{ m s}^{-1}$$. The coefficient of friction between the conveyor belt and bag is $$0.4$$. Initially, the bag slips on the belt before it stops due to friction. The distance travelled by the bag on the belt during slipping motion is: [Take $$g = 10 \text{ m s}^{-2}$$]

A block of mass $$M$$ slides down on a rough inclined plane with constant velocity. The angle made by the incline plane with horizontal is $$\theta$$. The magnitude of the contact force will be :

The velocity of a small ball of mass 0.3 g and density 8 g cc$$^{-1}$$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is 1.3 g cc$$^{-1}$$, then the value of viscous force acting on the ball will be $$x \times 10^{-4}$$ N, the value of x is _____ [use $$g = 10$$ m s$$^{-2}$$]

A block of mass $$m$$ slides along a floor while a force of magnitude $$F$$ is applied to it at an angle $$\theta$$ as shown in figure. The coefficient of kinetic friction is $$\mu_K$$. Then, the block's acceleration $$a$$ is given by: ($$g$$ is acceleration due to gravity)

When a body slides down from rest along a smooth inclined plane making an angle of 30° with the horizontal, it takes time $$T$$. When the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it takes time $$\alpha T$$, where $$\alpha$$ is a constant greater than 1. The co-efficient of friction between the body and the rough plane is $$\frac{1}{\sqrt{x}} \cdot \frac{\alpha^2-1}{\alpha^2}$$ where $$x$$ = _________.

A small block starts slipping down from a point B on an inclined plane AB, which is making an angle $$\theta$$ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction $$\mu$$. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If $$BC = 2AC$$, the coefficient of friction is given by $$\mu = k \tan\theta$$. The value of $$k$$ is ___________.

A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be:

Consider a block and trolley system as shown in figure. If the coefficient of kinetic friction between the trolley and the surface is $$0.04$$, the acceleration of the system in m s$$^{-2}$$ is: (Consider that the string is massless and unstretchable and the pulley is also massless and frictionless):

Given below are two statements :
Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials.
Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials.
In the light of the above statements, choose the most appropriate answer from the options given below :

A block of mass $$100$$ kg slides over a distance of $$10$$ m on a horizontal surface. If the co-efficient of friction between the surfaces is $$0.4$$, then the work done against friction (in J) is:

A small ball of mass $$m$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_0$$. After sometime, the ball falls with constant velocity. The viscous force on the ball is :

A block of mass 5 kg is placed on a rough inclined surface as shown in the figure. If $$\vec{F_1}$$ is the force required to just move the block up the inclined plane and $$\vec{F_2}$$ is the force required to just prevent the block from sliding down, then the value of $$|\vec{F_1}| - |\vec{F_2}|$$ is: [Use $$g = 10$$ m s$$^{-2}$$]

An object of mass $$5$$ kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of $$10$$ N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use $$g = 10$$ m s$$^{-2}$$]

A block of mass $$10$$ kg starts sliding on a surface with an initial velocity of $$9.8$$ ms$$^{-1}$$. The coefficient of friction between the surface and block is $$0.5$$. The distance covered by the block before coming to rest is : [use $$g = 9.8$$ ms$$^{-2}$$]

A water drop of radius $$1 \mu$$m falls in a situation where the effect of buoyant force is negligible. Co-efficient of viscosity of air is $$1.8 \times 10^{-5}$$ N s m$$^{-2}$$ and its density is negligible as compared to that of water $$10^6$$ g m$$^{-3}$$. Terminal velocity of the water drop is
(Take acceleration due to gravity $$= 10$$ m s$$^{-2}$$)

A block of mass 5 kg is placed at rest on a table of rough surface. Now, if a force of 30 N is applied in the direction parallel to surface of the table, the block slides through a distance of 50 m in an interval of time 10 s. Coefficient of kinetic friction is (given, $$g = 10$$ m s$$^{-2}$$):

A block of mass $$10 \,\, \text{kg}$$ is placed on a rough horizontal surface having a coefficient of static friction $$\mu_s = 0.6$$ and a coefficient of kinetic friction $$\mu_k = 0.4$$. If a horizontal force of $$50 \,\, \text{N}$$ is applied to the block, the magnitude of the frictional force acting on the block is:

(Take acceleration due to gravity $$g = 10 \,\, \text{m s}^{-2}$$)

A block takes $$t$$ time to slide down a plane inclined at 45° to the horizontal. If the surface is made smooth (frictionless), the block takes time $$\dfrac{t}{2}$$ to slide down the plane. The coefficient of friction between the block and the inclined plane is $$\left(\dfrac{\alpha}{100}\right)$$. The value of $$\alpha$$ is __________.

A smooth block is released at rest on a $$45^\circ$$ incline and then slides a distance $$d$$. The time taken to slide is $$n$$ times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

A given object takes n times the time to slide down $$45°$$ rough inclined plane as it takes the time to slide down an identical perfectly smooth $$45°$$ inclined plane. The coefficient of kinetic friction between the object and the surface of inclined plane is :

A block starts moving up an inclined plane of inclination 30° 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:

A block of mass 10 kg is kept on a rough inclined plane as shown in the figure. A force of 3 N is applied on the block. The coefficient of static friction between the plane and the block is 0.6. What should be the minimum value of force P, such that the block does not move downward? (take $$g = 10 \; ms^{-2}$$)

A block of mass 5 kg is moving on an inclined plane which makes an angle of 30° with the horizontal. Friction coefficient between the block and inclined plane surface is $$\frac{\sqrt{3}}{2}$$. The force to be applied on the block so that the block will move down without acceleration is _______N
$$(g=10m/s^{2})$$

An inclined plane is bent in such a way that the vertical cross-section is given by $$y = \frac{x^2}{4}$$ where $$y$$ is in vertical and $$x$$ in horizontal direction. If the upper surface of this curved plane is rough with coefficient of friction $$\mu = 0.5$$, the maximum height in cm at which a stationary block will not slip downward is ______ cm.

A particle of mass m falls from rest through a resistive medium having resistive force, F = -kv, where v is the velocity of the particle and k is a constant. Which of the following graphs represents velocity (v) versus time (t)?

Given below are two statements :
Statement (I) : The limiting force of static friction depends on the area of contact and independent of materials.
Statement (II) : The limiting force of kinetic friction is independent of the area of contact and depends on materials.
In the light of the above statements, choose the most appropriate answer from the options given below :

As shown in the figure a block of mass 10 kg lying on a horizontal surface is pulled by a force F acting at an angle $$30°$$, with horizontal. For $$\mu_s = 0.25$$, the block will just start to move for the value of $$F$$: [Given $$g = 10 \text{ m} \cdot \text{s}^{-2}$$]