Laws of Motion — JEE Main PYQs

A simple pendulum has a bob with mass $m$ and charge q . The pendulum string has negligible mass. When a uniform and horizontal electric field $\vec{E}$ is applied, the tension in the string changes. The final tension in the string, when pendulum attains an equilibrium positi …

A large drum having radius R is spinning around its axis with angular velocity $\omega$, as shown in figure. The minimum value of $\omega$ so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mas …

A spring of force constant $15\mathrm{N}/\mathrm{m}$ is cut into two pieces. If the ratio of their length is $1:3$, then the force constant of smaller piece is ______ $\mathrm{N}/\mathrm{m}$

In the given figure the blocks A, B and C weigh 4 kg, 6 kg and 8 kg respectively. The co-efficient of sliding friction between any two surfaces is 0.5. The force $\overrightarrow{\mathrm{F}}$ required to slide the block C with constant speed is ______ N. (Used …

A block of mass 5 kg is moving on an inclined plane which makes an angle of $30^{\circ }$ 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 witho …

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

A flexible chain of mass $m$ hangs between two fixed points at the same level. The inclination of the chain with the horizontal at the two points of support is $30^{\circ }$. Considering the equilibrium of each half of the chain, the tension of the chain at the lowest point is ___ …

A small block of mass $m$ slides down from the top of a frictionless inclined surface, while the inclined plane is moving towards left with constant acceleration ${\mathrm{a}}_0$. The angle between the inclined plane and ground is $\theta$ and its base length is L . Assuming that …

A 4 kg mass moves under the influence of a force $\vec{F}=\left(4t^3\hat{i}-3t\hat{j}\right)N$ where $t$ is the time in second.
If mass starts from origin at $\mathrm{t}=0$, the velocity and position after $\mathrm{t}=2\mathrm{s}$ will be :

A 0.5 kg mass is in contact against the inner wall of a cylindrical drum of radius 4 m rotating about its vertical axis. The minimum rotational speed of the drum to enable the mass to remain stuck to the wall (without falling) is $5\mathrm{rad}/\mathrm{s}$. The coefficient o …

The time taken by a block of mass $m$ to slide down from the highest point to the lowest point on a rough inclined plane is $50\%$ more compared to the time taken by the same block on identical inclined smooth plane. Both inclined planes are at $45^{\circ }$ with the horizontal. T …

At $t=0$, a body of mass 100 g starts moving under the influence of a force $(5\hat{\mathrm{i}}+10\hat{\mathrm{j}})\mathrm{N}$. After 2 s its position is $(2x\hat{\mathrm{i}}+5y\hat{\mathrm{j}})\mathrm{m}$. The ratio $\mathrm{x}:\mathrm{y}$ is $\_\_\_\_$ .

Three masses ${\mathrm{m}}_1=4$ kg, ${\mathrm{m}}_2=4$ kg and ${\mathrm{m}}_3=6$ kg are suspended from a fixed smooth frictionless pully as shown in the figure below. The value of ${\mathrm{T}}_1/{\mathrm{T}}_2$ is ______. (take $\mathrm{g}=10$ m/s${}^2$)

A wedge Y with mass of 10 kg and all frictionless surfaces and the inclined surface making $37^{\circ }$ with horizontal. A block X with mass 2 kg is placed at the highest point of the wedge as shown in figure is at rest. At $\mathrm{t}=0$ wedge (Y) is pulled toward right with con …

Two blocks (P and Q) with respectively masses 2 kg and 1.5 kg are joined by a massless thread. These blocks are mounted on a frictionless pully which is fixed on the edge of a cube (S), as shown in the figure below. Block P is positioned on the top surface which has no friction a …

A block takes $t$ time to slide down a plane inclined at $45^{\circ }$ to the horizontal. If the surface is made smooth (frictionless), the block takes time $\frac{\mathrm{t}}{2}$ to slide down the plane. The coefficient of friction between the block and the inclined plane is …

A car moving with a speed of $54\mathrm{km}/\mathrm{h}$ takes a turn of radius 20 m. A simple pendulum is suspended from the ceiling of the car. Determine the angle made by the string of the pendulum with the vertical during the turning. (Take …

A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is …

A massless spring gets elongated by amount $x_1$ under a tension of 5 N . Its elongation is $x_2$ under the tension of 7 N . For the elongation of $(5x_1-2x_2)$, the tension in the spring will be,

A balloon and its content having mass M is moving up with an acceleration ' a '. The mass that must be released from the content so that the balloon starts moving up with an acceleration '3a' will be : (Take ' g ' as acceleration due to gravity)

A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes $\left(\frac{3}{\pi }\right)$ rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is ______ ML.

A car of mass 'm' moves on a banked road having radius 'r' and banking angle $\theta$. To avoid slipping from banked road, the maximum permissible speed of the car is ${\mathrm{v}}_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is :-

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitude of tensions ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, respectively, are (in N) :

A body of mass $m$ is suspended by two strings making angles ${\theta }_1$ and ${\theta }_2$ with the horizontal ceiling with tensions ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ simultaneously. ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ are related by $T_1=\sqrt{3}{T}_2$. the angles …

An object with mass 500 g moves along x -axis with speed $\mathrm{v}=4\sqrt{\mathrm{x}}\mathrm{m}/\mathrm{s}$. The force acting on the object is :

A cubic block of mass $m$ is sliding down on an inclined plane at $60^{\circ }$ with an acceleration of $\frac{g}{2}$, the value of coefficient of kinetic friction is

A body of mass 2 kg moving with velocity of ${\overrightarrow{\mathrm{v}}}_{\mathrm{in}}=3\hat{\mathrm{i}}+4\hat{\mathrm{j}}{\mathrm{ms}}^{-1}$ enters into a constant force field of 6 N directed along positive z-axis. If the body remains in the field for a period of $\frac{5}{3}$ …

A car of 800 kg is taking turn on a banked road of radius 300 m and angle of banking $30^{\circ }$. If coefficient of static friction is 0.2 then the maximum speed with which car can negotiate the turn safely: …

A body of weight 200 N is suspended from a tree branch through a chain of mass 10 kg . The branch pulls the chain by a force equal to (if $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ ):

A 2 kg brick begins to slide over a surface which is inclined at an angle of $45^{\circ }$ with respect to horizontal axis. The co-efficient of static friction between their surfaces is :

A wooden block, initially at rest on the ground, is pushed by a force which increases linearly with time t . Which of the following curve best describes acceleration of the block with time :

A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

A wooden block of mass 5 kg rests on soft horizontal floor. When an iron cylinder of mass 25 kg is placed on the top of the block, the floor yields and the block and the cylinder together go down with an acceleration of $0.1{\mathrm{ms}}^{-2}$. The action force of the system on t …

Three blocks ${\mathrm{M}}_1$, ${\mathrm{M}}_2$, ${\mathrm{M}}_3$ having masses $4\mathrm{kg}$, $6\mathrm{kg}$ and $10\mathrm{kg}$ respectively are hanging from a smooth pully using rope 1, 2 and 3 as shown in figure. The tension in the rope $1$, $T_1$ when they are movin …

A light string passing over a smooth light pulley connects two blocks of masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$ (where ${\mathrm{m}}_2>{\mathrm{m}}_1$). If the acceleration of the system is $\frac{\mathrm{g}}{\sqrt{2}}$, then the ratio of the masses …

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

A light unstretchable string passing over a smooth light pulley connects two blocks of masses ${\mathrm{m}}_1$ and ${\mathrm{m}}_2$. If the acceleration of the system is $\frac{\mathrm{g}}{8}$, then the ratio of the masses $\frac{{\mathrm{m}}_2}{{\mathrm{m}}_1}$ is:

A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle $\theta$ with the horizontal. The weight experienced by the person is:

A 1 kg mass is suspended from the ceiling by a rope of length 4 m . A horizontal force ' F ' is applied at the mid point of the rope so that the rope makes an angle of $45^{\circ }$ with respect to the vertical axis as shown in figure. The magnitude of F is :

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 …

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle $60^{\circ }$ with the horizontal, the weight experienced by the man is :

A stone of mass 900 g is tied to a string and moved in a vertical circle of radius 1 m making 10 rpm. The tension in the string, when the stone is at the lowest point is (if ${\pi }^2=9.8$ and $g=9.8$ m/s${}^2$)

A train is moving with a speed of $12\mathrm{m}/\mathrm{s}$ on rails which are 1.5 m apart. To negotiate a curve radius 400 m , the height by which the outer rail should be raised with respect to the inner rail is (Given, $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$) :

If the radius of curvature of the path of two particles of same mass are in the ratio $3:4$, then in order to have constant centripetal force, their velocities will be in the ratio of:

In the given arrangement of a doubly inclined plane two blocks of masses M and m are placed. The blocks are connected by a light string passing over an ideal pulley as shown. The coefficient of friction between the surface of the plane and the blocks is 0.25. The value of m, for …

A coin is placed on a disc. The coefficient of friction between the coin and the disc is $\mu$. If the distance of the coin from the center of the disc is $r$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is:

A body of mass 4 kg experiences two forces ${\overrightarrow{\mathrm{F}}}_1=5\hat{\mathrm{i}}+8\hat{\mathrm{j}}+7\hat{\mathrm{k}}$ and ${\overrightarrow{\mathrm{F}}}_2=3\hat{\mathrm{i}}-4\hat{\mathrm{j}}-3\hat{\mathrm{k}}$. The acceleration acting on the body is :

Suppose a uniformly charged wall provides a uniform electric field of $2\times 10^4\mathrm{N}/\mathrm{C}$ normally. A charged particle of mass 2 g being suspended through a silk thread of length 20 cm and remain stayed at a distance of 10 cm from the wall. Then the charge …

A ball of mass 0.5 kg is attached to a string of length 50 cm. The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can bear is 400 N. The maximum possible value of angular velocity of the ball in rad/s is,:

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 ${\mathrm{ms}}^{-2}$ is :
(Consider that the string is massless and unstretchable and the pulley is also …