Laws of Motion — JEE Main PYQs

A person is standing in an elevator. In which situation, he experiences weight loss ?

A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is $\alpha$ with respect to point P. Which of the following graph …

A system of two blocks of masses $\mathrm{m}=2\mathrm{kg}$ and $\mathrm{M}=8\mathrm{kg}$ 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 …

A smooth circular groove has a smooth vertical wall as shown in figure. A block of mass m moves against the wall with a speed v . Which of the following curve represents the correct relation between the normal reaction on the block by the wall ( N ) and speed of the block (v) ?

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

A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N . If the maximum speed with which the stone can revolve is $\frac{\mathrm{K}}{\pi }\mathrm{rev}./\min$. T …

A stone of mass m , tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is :

A disc with a flat small bottom beaker placed on it at a distance R from its center is revolving about an axis passing through the center and perpendicular to its plane with an angular velocity $\omega$. The coefficient of static friction between the bottom of the beaker and th …

A curve in a level road has a radius 75 m. The maximum speed of a car turning this curved road can be $30\mathrm{m}/\mathrm{s}$ without skidding. If radius of curved road is changed to 48 m and the coefficient of friction between the tyres and the road remains same, then maxi …

A block of mass 200 g is kept stationary on a smooth inclined plane by applying a minimum horizontal force $\mathrm{F}=\sqrt{\mathrm{x}}\mathrm{N}$ as shown in figure. The value of $x=$ _____.

A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from …

The coefficient of static friction between a wooden block of mass 0.5 kg and a vertical rough wall is 0.2. The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall be ______ N.
[$g=10$ ms${}^{-2}$]

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 …

A particle of mass $m$ is suspended form a ceiling through a string of length $L$. The particle moves in a horizontal circle of radius $r$ such that $r=\frac{L}{\sqrt{2}}$. The speed of particle will be:

Two blocks of masses 3 kg and 5 kg are connected by a metal wire going over a smooth pulley. The breaking stress of the metal is $\frac{24}{\pi }\times 10^2{\mathrm{Nm}}^{-2}$. What is the minimum radius of the wire? (take $\mathrm{g}=10{\mathrm{ms}}^{-2}$ )

The coefficient of static friction between two blocks is 0.5 and the table is smooth. The maximum horizontal force that can be applied to move the blocks together is _____ N. (take $\mathrm{g}=10{\mathrm{ms}}^{-2}$)

The normal reaction 'N' for a vehicle of 800 kg mass, negotiating a turn on a $30^{\circ }$ banked road at maximum possible speed without skidding is $\_\_\_\_$ $\times 10^3\mathrm{kg}\mathrm{m}/{\mathrm{s}}^2$.
[Given $\cos 30^{\circ }=0.87,{\mu }_5=0.2$]

A steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration $0.2\mathrm{m}/{\mathrm{s}}^2$. The normal reaction ${\mathrm{R}}^{\prime }$ by the floor if mass of the iro …

A body of mass ' $m$ ' is launched up on a rough inclined plane making an angle of $30^{\circ }$ with the horizontal. The coefficient of friction between the body and plane is $\frac{\sqrt{x}}{5}$ if the time of ascent is half of the time of descent. The value of $x$ is __ …

The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

As shown in the figure, a block of mass $\sqrt{3}\mathrm{kg}$ is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3\sqrt{3}}$. The critical force to be applied on the vertical surface as shown at an angle $60^{\circ }$ with horizontal such that it does no …

A person standing on a balance inside a stationary lift measures 60 kg . The weight of that person if the lift descends with uniform downward acceleration of $1.8\mathrm{m}/{\mathrm{s}}^2$ will be ____ $\mathrm{N}.\left[\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2\right]$

An inclined plane making an angle of $30^{\circ }$ with the horizontal is placed in a uniform horizontal electric field $200\frac{\mathrm{N}}{\mathrm{C}}$ as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the co …

Two masses $A$ and $B$, each of mass $M$ are fixed together by a massless spring. A force acts on the mass B as shown in figure. If the mass $A$ starts moving away from mass $B$ with acceleration '$a$', then the acceleration of mass $B$ will be:

Statement-1: If three forces ${\vec{F}}_1,{\vec{F}}_2$ and ${\vec{F}}_3$ are represented by three sides of a triangle and, ${\vec{F}}_1+{\vec{F}}_2=-{\vec{F}}_3$, then these three forces are concurrent forces and satisfy the condition for equilibrium.
Statement-II: A trian …

A car is moving on a plane inclined at $30^{\circ }$ to the horizontal with an acceleration of $10{\mathrm{ms}}^{-2}$ parallel to the plane upward. A bob is suspended by a string from the roof of the car. The angle in degrees which the string makes with the vertical is _____. (Tak …

A modern grand - prix racing car of mass $m$ is traveling on a flat track in a circular arc of radius R with a speed u . If the coefficient of static between the tyres and the track is ${\mu }_s$, then the magnitude of negative lift $F_L$ acting downwards on the car is :
( …

Two blocks ( $\mathrm{m}=0.5\mathrm{kg}$ and $\mathrm{M}=4.5\mathrm{kg}$ ) are arranged on a horizontal frictionless table as shown in figure. The coefficient of static friction between the two blocks is $\frac{3}{7}$. Then the maximum horizontal force that can be appli …

A force $\vec{F}=(40\hat{i}+10\hat{j})\mathrm{N}$ acts on a body of mass 5 kg. If the body starts from rest, its position vector $\overrightarrow{\mathrm{r}}$ at time $\mathrm{t}=10\mathrm{s}$, will be :

A small block slides down from the top of hemisphere of radius $R=3\mathrm{m}$ as shown in the figure. The height ' $h$ ' at which the block will lose contact with the surface of the sphere is ____ m.
(Assume there is no friction between the block and the hemisphere)

A block of mass $m$ slides on the wooden wedge, which in turn slides backward on the horizontal surface. The acceleration of the block with respect to the wedge is: Given $\mathrm{m}=8\mathrm{kg},\mathrm{M}=$ 16 kg Assume all the surfaces shown in the figure to be frictionless …

An object of mass '$m$' is being moved with a constant velocity under the action of an applied force of 2 N along a frictionless surface with following surface profile.

The correct applied force vs distance graph will be:

When a body slides down from rest along a smooth inclined plane making an angle of $30^{\circ }$ with the horizontal, it takes time T. When the same body slides down from the rest along a rough inclined plane making the same angle and through the same distance, it takes time …

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 is ${\mu }_{\mathrm{K}}$. Then, the block's acceleration '$a$' is given by :
( g is acceleration due to gravity)

A block of 200 g mass moves with a uniform speed in a horizontal circular groove, with vertical side walls of radius 20 cm . If the block takes 40 s to complete one round, the normal force by the side walls of the groove is:

Statement I : A cyclist is moving on an un-banked road with a speed of $7{\mathrm{kmh}}^{-1}$ and takes a sharp circular turn along a path of radius of 2 m without reducing the speed. The static friction coefficient is 0.2 The cyclist will not slip and pass the curve. ( …

A body of mass 2 kg moves under a force of $(2\hat{\mathrm{i}}+3\hat{\mathrm{j}}+5\hat{\mathrm{k}})\mathrm{N}$. It starts from rest and was at the origin initially. After 4 s , its new coordinates are ( $8,b,20$ ). The value of $b$ is ____ (Round off the Nearest Integer …

A body of mass 1 kg rests on a horizontal floor with which it has a coefficient of static friction $\frac{1}{\sqrt{3}}$. It is desired to make the body move by applying the minimum possible force F N. The value of $F$ will be ______ (Round off to Nearest Integer)
[Take …

A boy of mass 4 kg is standing on a piece of wood having mass 5 kg. If the coefficient of friction between the wood and the floor is 0.5, the maximum force that boy can exert on the rope so that the piece of wood does not move from its place is ______ N. (Round off to the Nearest …

A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is $10\mathrm{m}/\mathrm{s}$ and slows down with uniform deceleration, then magnitude effective …

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of $45^{\circ }$ with the vertical. Then F equals: (Take $\mathrm{g}=10{\mathrm{ms}}^{-2}$ and t …

A spring mass system (mass m, spring constant k and natural length $\ell$) rests in equilibrium on a horizontal disc. The free end of the spring is fixed at the centre of the disc. If the disc together with spring mass system, rotates about its axis with an angular velocity …

A body of mass $\mathrm{m}=10\mathrm{kg}$ is attached to one end of a wire of length 0.3 m. The maximum angular speed (in $\mathrm{rad}{\mathrm{s}}^{-1}$) with which it can be rotated about its other end in space station is (Breaking stress of wire …

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 …

An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height $h$ from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is: …

A small ball of mass $m$ is thrown upward with velocity $u$ from the ground. The ball experiences a resistive force $mk{v}^2$ where $v$ is its speed. The maximum height attained by the ball is:

The bob of a simple pendulum has mass 2 g and a charge of $5.0\mu \mathrm{C}$. It is at rest in a uniform horizontal electric field of intensity $2000\frac{\mathrm{V}}{\mathrm{m}}$. At equilibrium, the angle that the pendulum makes with the vertical is: (take …

Two blocks $A$ and $B$ of masses $m_A=1\mathrm{kg}$ and $m_B=3\mathrm{kg}$ are kept on the table as shown in figure. The coefficient of friction between A and B is 0.2 and between B and the surface of the table is also 0.2. The maximum force $F$ that can be applied on $B$ …

A block of mass 5 kg is (i) pushed in case (A) and (ii) pulled in case (B), by a force $\mathrm{F}=$ 20 N , making an angle of $30^{\circ }$ with the horizontal, as shown in the figures. The coefficient of friction between the block and floor is $\mathrm{m}=0.2$. The difference be …

A smooth wire of length $2\pi \mathrm{r}$ is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed w about the vertical diameter AB , as shown in figure, the bead is at rest with respect to the ci …