Laws of Motion — JEE Main PYQs

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

Three blocks A, B and C are pulled on a horizontal smooth surface by a force of 80 N as shown in figure

The tensions ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ in the string are respectively:

All surfaces shown in figure are assumed to be frictionless and the pulleys and the string are light. The acceleration of the block of mass 2 kg is :

A light string passing over a smooth light fixed pulley connects two blocks of masses $m_1$ and $m_2$. If the acceleration of the system is $g/8$, then the ratio of masses is

A block of mass 5 kg is placed on a rough inclined surface as shown in the figure.
If ${\overrightarrow{F}}_1$ is the force required to just move the block up the inclined plane and ${\overrightarrow{F}}_2$ is the force required to just prevent the block from sliding down, then t …

At any instant the velocity of a particle of mass 500 g is $\left(2t\hat{\mathrm{i}}+3{\mathrm{t}}^2\hat{\mathrm{j}}\right){\mathrm{ms}}^{-1}$. If the force acting on the particle at $\mathrm{t}=1\mathrm{s}$ is …

A child of mass 5 kg is going round a merry-go-round that makes 1 rotation in 3.14 s. The radius of the merry-go-round is 2 m. The centrifugal force on the child will be

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: An electric fan continues to rotate for some time after the current is switched off.
Reason R: Fan continuous to rotate due to inertia of motion.
In the light of abo …

A coin placed on a rotating table just slips when it is placed at a distance of 1 cm from the center. If the angular velocity of the table in halved, it will just slip when placed at a distance of ______ from the centre:

Three force $F_1=10\text{ N}$, $F_2=8\text{ N}$, $F_3=6\text{ N}$ are acting on a particle of mass 5 kg. The forces $F_2$ and $F_3$ are applied perpendicular so that particle remains at rest. If the force $F_1$ is removed, then the acceleration of the particle is:

A vehicle of mass 200 kg is moving along a levelled curved road of radius 70 m with angular velocity of $0.2\mathrm{rad}/\mathrm{s}$. The centripetal force acting on the vehicle is :

A small block of mass 100 g is tied to a spring of spring constant $7.5\mathrm{N}/\mathrm{m}$ and length 20 cm. The other end of spring is fixed at a particular point A. If the block moves in a circular path on a smooth horizontal surface with constant angular velocity …

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 10s. Coefficient of kinetic friction is (given, …

Given below are two statements :

Statement-I : An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable.
Statement-II : Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight …

As per given figure, a weightless pulley P is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

A spherical body of mass 2 kg starting from rest acquires a kinetic energy of 10000 J at the end of $5^{\text{th }}$ second. The force acted on the body is ____ N.

A body of mass 200 g is tied to a spring of spring constant $12.5$ N/m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed $5$ rad/s, then the ratio of extension in the spring …

A car is moving with a constant speed of 20 $\mathrm{m}/\mathrm{s}$ in a circular horizontal track of radius 40 m. A bob is suspended from the roof of the car by a massless string. The angle made by the string with the vertical will be : (Take …

Consider a block kept on an inclined plane (inclined at $45^{\circ }$ ) as shown in the figure. If the force required to just push it up the incline is 2 times the force required to just prevent it from sliding down, the coefficient of friction between the block and inclined pla …

A block of mass $m$ slides down the plane inclined at angle $30^{\circ }$ with an acceleration $\frac{\mathrm{g}}{4}$. The value of coefficient of kinetic friction will be :

A car is moving on a horizontal curved road with radius 50 m . The approximate maximum speed of car will be, if friction between tyres and road is 0.34 . [Take $\mathrm{g}=10{\mathrm{ms}}^{-2}$ ]

The time taken by an object to slide down $45^{\circ }$ rough inclined plane is $n$ times as it takes to slide down a perfectly smooth $45^{\circ }$ incline plane. The coefficient of kinetic friction between the object and the incline plane is

Force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes 50 m in the next 10 s. The value of force will be:

An object moves at a constant speed along a circular path in a horizontal plane with centre at the origin. When the object is at $\mathrm{x}=+2\mathrm{m}$, its velocity is $-4\hat{\mathrm{j}}\mathrm{m}/\mathrm{s}$. The object's velocity (v) and acceleration (a) at …

A block of $\sqrt{3}\mathrm{kg}$ is attached to a string whose other end is attached to the wall. An unknown force F is applied so that the string makes an angle of $30^{\circ }$ with the wall. The tension T is :
(Given $\mathrm{g}=10{\mathrm{ms}}^{-2}$)

The figure represents the momentum time (p-t) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively?
If $(t_3-t_2)<t_1$.

As shown in figure, a 70 kg garden roller is pushed with a force of $\overrightarrow{\mathrm{F}}=200\mathrm{N}$ at an angle of $30^{\circ }$ with horizontal. The normal reaction on the roller is (Given $\mathrm{g}=10\mathrm{m}{\mathrm{s}}^{-2}$)

A stone of mass 1 kg is tied to end of a massless string of length 1 m. If the breaking tension of the string is 400 N, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is:

A body of mass 10 kg is moving with an initial speed of $20m/s$. The body stops after 5 s due to friction between body and the floor. The value of the coefficient of friction is: (Take acceleration due to gravity $g=10{\mathrm{ms}}^{-2}$)

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 $30^{\circ }$, with horizontal. For ${\mu }_s=0.25$, the block will just start to move for the value of F: [Given $g=10{\mathrm{ms}}^{-2}$]

Two bodies of masses ${\mathrm{m}}_1=5\mathrm{kg}$ and ${\mathrm{m}}_2=3\mathrm{kg}$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the b …

A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $\mathrm{x}\sqrt{\mathrm{F}}\mathrm{rad}{\mathrm{s}}^{-1}$. If F …

A metal wire of length 0.5 m and cross-sectional area $10^{-4}{\mathrm{m}}^2$ has breaking stress $5\times 10^8{\mathrm{Nm}}^{-2}$. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be \ …

A uniform metal chain of mass m and length ' L ' passes over a massless and frictionless pulley. It is released from rest with a part of its length ' $l$ ' is hanging on one side and rest of its length ' $\mathrm{L}-l$ ' is hanging on the other side of the pulley. At a certai …

A uniform electric field $\mathrm{E}=(8\mathrm{m}/\mathrm{e})\mathrm{V}/\mathrm{m}$ is created between two parallel plates of length 1 m as shown in figure, (where $\mathrm{m}=$ mass of electron and $\mathrm{e}=$ charge of electron). An electron enters the field symm …

A bag is gently dropped on a conveyor belt moving at a speed of $2\mathrm{m}/\mathrm{s}$. 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 bel …

Four forces are acting at a point P in equilibrium as shown in figure. The ratio of force ${\mathrm{F}}_1$ to ${\mathrm{F}}_2$ is $1:\mathrm{x}$ where $\mathrm{x}=$ ______.

Two masses $M_1$ and $M_2$ are tied together at the two ends of a light inextensible string that passes over a frictionless pulley. When the mass $M_2$ is twice that of $M_1$, the acceleration of the system is $a_1$. When the mass $M_2$ is thrice that of $M_1$, the acceleration o …

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 :

For a free body diagram shown in the figure, the four forces are applied in the ' x ' and ' y ' directions. What additional force must be applied and at what angle with positive x -axis so that the net acceleration of body is zero?

Three masses $\mathrm{M}=100\mathrm{kg},{\mathrm{m}}_1=10\mathrm{kg}$ and ${\mathrm{m}}_2=20\mathrm{kg}$ are arranged in a system as shown in figure. All the surfaces are frictionless and strings are inextensible and weightless. The pulleys are also weightless and fri …

A monkey of mass 50 kg climbs on a rope which can withstand the tension (T) of 350N. If monkey initially climbs down with an acceleration of $4\mathrm{m}/{\mathrm{s}}^2$ and then climbs up with an acceleration of $5\mathrm{m}/{\mathrm{s}}^2$. Choose the correct option …

A $\sqrt{34}\mathrm{m}$ long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If ${\mathrm{F}}_{\mathrm{f}}$ and ${\mathrm{F}}_{\mathrm{w}}$ are the reaction forces of the floor and the wall, then ra …

One end of a massless spring of spring constant k and natural length $l_0$ is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity …

A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $\theta ={\tan }^{-1}\left(\mathrm{x}\times 10^{-1}\right)$. The …

A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $\frac{\mathrm{X}}{5}$ Mg for …

A block of mass 40 kg slides over a surface, when a mass of 4 kg is suspended through an inextensible massless string passing over frictionless pulley as shown below. The coefficient of kinetic friction between the surface and block is 0.02 . The acceleration of block is. (Given …

A block of mass M placed inside a box descends vertically with acceleration ' a '. The block exerts a force equal to one-fourth of its weight on the floor of the box. The value of ' $a$ ' will be :

In the arrangement shown in figure ${\mathrm{a}}_1,{\mathrm{a}}_2,{\mathrm{a}}_3$ and ${\mathrm{a}}_4$ are the accelerations of masses $m_1,m_2,m_3$ and $m_4$ respectively. Which of the following relation is true for this arrangement?

A system to 10 balls each of mass 2 kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the $7^{\text{th}}$ and $8^{\text{th}}$ ball is _____ N when …