JEE Laws of Motion PYQs with Solutions PDF, Download Now

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

In the given figure, the blocks A, B and C weigh 4 kg, 6 kg and 8 kg, respectively. The coefficient of sliding friction between any two surfaces is 0.5. The force F required to slide the block C with constant speed is __ N. (Use $$g=10m/s^{2}$$)

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 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)?

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
$$(g=10m/s^{2})$$

A body of mass 14 kg initially at rest explodes and breaks into three fragments of masses in the ratio 2 : 2 : 3. The two pieces of equal masses fly off perpendicular to each other with a speed of 18 m/s each. The velocity of the heavier fragment is ______m/s.

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 $$a_{0}$$. The angle between U1e inclined plane and ground is O and its base length is L. Assuming that initially the small block is at the top of the inclined plane, the time it takes to reach the lowest point of the inclined plane 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,

$$\text{A string of length } L \text{ is fixed at one end and carries a mass of } M\text{ at the other end. }\text{The mass makes } \left(\frac{3}{\pi}\right)\text{ rotations per second about the vertical axis passing through end of the string as shown. }\text{The tension in the string is } \underline{\hspace{2cm}} ML.$$

Two cars P and Q are moving on a road in the same direction. Accleration of car P increases linearly with
time whereas car Q moves with a constant accleration. Both cars cross each other at time t=0, for the first
time. The maximum possible number of crossing(s) (including the crossing at t=0) 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:

Two forces $$\vec{F_1}$$ and $$\vec{F_2}$$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $$\vec{F_1}$$ and $$\vec{F_2}$$ is $$\cos^{-1}\left(\frac{1}{n}\right)$$. The value of |n| is _____.

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)

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):

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$$^{-1}$$ is :

The identical spheres each of mass $$2M$$ are placed at the corners of a right angled triangle with mutually perpendicular sides equal to $$4$$ m each. Taking point of intersection of these two sides as origin, the magnitude of position vector of the centre of mass of the system is $$\frac{4\sqrt{2}}{x}$$, where the value of $$x$$ is ________.

A cricket player catches a ball of mass 120 g moving with $$25 \text{ m s}^{-1}$$ speed. If the catching process is completed in 0.1 s then the magnitude of force exerted by the ball on the hand of player will be (in SI unit):

A body of mass 4 kg experiences two forces $$\vec{F_1} = 5\hat{i} + 8\hat{j} + 7\hat{k}$$ and $$\vec{F_2} = 3\hat{i} - 4\hat{j} - 3\hat{k}$$. The acceleration acting on the body is:

A train is moving with a speed of $$12 \text{ m s}^{-1}$$ 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, $$g = 10 \text{ m s}^{-2}$$):

A body of mass $$1000$$ kg is moving horizontally with a velocity $$6 \text{ m s}^{-1}$$. If $$200$$ kg extra mass is added, the final velocity (in $$\text{m s}^{-1}$$) 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 the above statements, choose the most appropriate answer from the options given below :

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:

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 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 $$g = 9.8 \text{ m s}^{-2}$$)

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 $$2 \text{ kg}$$ is

A spherical body of mass $$100 \text{ g}$$ is dropped from a height of $$10 \text{ m}$$ from the ground. After hitting the ground, the body rebounds to a height of $$5 \text{ m}$$. The impulse of force imparted by the ground to the body is given by: (given $$g = 9.8 \text{ m s}^{-2}$$)

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 $$T_1$$ and $$T_2$$ in the string are respectively:

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:

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 which $$M = 10$$ kg will move down with an acceleration of $$2 \text{ m s}^{-2}$$, is: (take $$g = 10 \text{ m s}^{-2}$$ and $$\tan 37° = \frac{3}{4}$$)

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 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 $$\frac{g}{8}$$, 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 $$\vec{F_1}$$ 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$$^{-2}$$]

Two blocks of mass 2 kg and 4 kg are connected by a metal wire going over a smooth pulley as shown in figure. The radius of wire is $$4.0 \times 10^{-5}$$ m and Young's modulus of the metal is $$2.0 \times 10^{11}$$ N m$$^{-2}$$. The longitudinal strain developed in the wire is $$\frac{1}{\alpha\pi}$$. The value of $$\alpha$$ is [Use $$g = 10$$ m s$$^{-2}$$]

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

A particle moves in $$x - y$$ plane under the influence of a force $$\vec{F}$$ such that its linear momentum is $$\vec{p}(t) = \hat{i} \cos(kt) - \hat{j} \sin(kt)$$. If $$k$$ is constant, the angle between $$\vec{F}$$ and $$\vec{p}$$ will be :

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

Three blocks $$M_1, M_2, M_3$$ having masses $$4 \text{ kg}, 6 \text{ kg}$$ and $$10 \text{ kg}$$ respectively are hanging from a smooth pulley using rope 1, 2 and 3 as shown in figure. The tension in the rope 1, $$T_1$$ when they are moving upward with acceleration of $$2 \text{ ms}^{-2}$$ is ______ N (if $$g = 10 \text{ m/s}^2$$).

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $$1/\theta$$ vs the resistance $$(R)$$ of the resistance box is shown in the figure. The figure of merit of the galvanometer is ______ $$\times 10^{-1} \text{ A/division}$$. [The source has emf 2V]

A train starting from rest first accelerates uniformly up to a speed of $$80 \text{ km/h}$$ for time $$t$$, then it moves with a constant speed for time $$3t$$. The average speed of the train for this duration of journey will be (in km/h) :

A light string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2$$ (where $$m_2>m_1$$). If the acceleration of the system is $$\frac{g}{\sqrt{2}}$$, then the ratio of the masses $$\frac{m_1}{m_2}$$ is:

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

A car of $$800 \text{ kg}$$ is taking turn on a banked road of radius $$300 \text{ m}$$ and angle of banking $$30°$$. If coefficient of static friction is $$0.2$$ then the maximum speed with which car can negotiate the turn safely: $$(g = 10 \text{ m/s}^2, \sqrt{3} = 1.73)$$

A player caught a cricket ball of mass $$150 \text{ g}$$ moving at a speed of $$20 \text{ m/s}$$. If the catching process is completed in $$0.1 \text{ s}$$, the magnitude of force exerted by the ball on the hand of the player 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 light unstretchable string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2$$. If the acceleration of the system is $$\frac{g}{8}$$, then the ratio of the masses $$\frac{m_2}{m_1}$$ is :

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

The magnitude of $$F$$ is : (Assume that the system is in equilibrium and $$g = 10 \text{ m/s}^2$$)

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 $$30°$$, with horizontal. For $$\mu_s = 0.25$$, the block will just start to move for the value of $$F$$: [Given $$g = 10 \text{ m} \cdot \text{s}^{-2}$$]

Figures (a), (b), (c) and (d) show variation of force with time

The impulse is highest in figure.

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 $$g = 10 \text{ m s}^{-2}$$)