Newton's law of motion Questions and Answers

3 0 5 sec Calculate the force of friction acting on the body of mass m placed over the inclined plane of friction co efficient u 0 8 34 2 3 mg 1 mg 5300 m mg 2 4 Zero 2

The mass of a box measured by a grocer s balance 23 kg Two gold pieces of masses 20 15 g and 20 17 are added to the box The total mass of the box is a 2 3 kg c 2 340 kg b 2 34 kg d 2 3403 kg

c mg 7 A lift is going up The total mass of the lift and the passe is 1500 kg The variation in the speed of the lift is as given in the graph The tension in the rope pulling the lift at 11th sec will be t speed in m sec 3 6 a 17400 N b 14700 N c 12000 N d Zero 2 10 12 8 In the above ques the height to which the lift takes the passenger is a 3 6 meters c 18 meters b 8 meters d 36 meters

C 6 A heavy block kept on a frictionless surface and being pulled by two ropes of equal mass m as show in figure At t 0 the force on the left rope is withdrawn but the force on the right end continues to ac Let F and F2 be the magnitudes of the forces by the right rope and the left rope on the blo respectively F A F F2 F fort 0 CLEEF F F fort 0 m ZZZZZ m 777F B F F2 F mg for t 0 D F F F F fort 0

2 Two persons are holding a light rope tightly at its ends so that it is horizontal A 15 kg weight is attached to the rope at the mid point which now no longer remains horizontal The minimum tension required to completely straighten the rope is A 15 kg C 5 kg 15 B kg 2 D Infinitely large or not possible

7 Two ships are 10 km apart on the west east line at some instant the first one steaming to the east at 30 km h and the other one to the north at 40 km h What is the closest distance between them and after what time this occurs 8 km 3 24 h

A particle of small mass m is joined to a very heavy body of mass M by a light string passing over a light frictionless pulley Both bodies are free to move The total downward force on the pulley is approximately 1 Question Type Single Correct Type 2 mg 2 Mg m 3 4 mg M

A small block of mass m is placed on a plank of mass 2m and length L A force F is applied as shown in the figure Find time taken by block A to reach end of plank B A m A C mL 2F 8mL VF B L B D 4mL F 4F F 19 A fanger Chrif B d am un A m C mL 2F 8mL VF B L B 2m D 4mL F F mL 4F F

Q Block A of mass m 2 is connected to one end of light rope which passes over a pulley as shown in Fig 6 50 A man of mass m climbs the other end of rope with a relative acceleration of g 6 with respect to rope Find the acceleration of block A and tension in the rope m 2 g 6 m

A cart of mass 3 kg is pulled by a 5kg object as shown The cart whose length is 40 cm moves along the table without friction There is a block of mass 2kg on the cart which falls from it 0 8s after the start of the motion Find the coefficient of kinetic friction between the cart and the brick Use g 10 m s Write the value of 10 2kg 3kg 3 3 kg 5kg ART T Chichest g 10 m s for f 40 cm at 10 2kg 3kg st 2kg

Consider the situation given in the diagram all surfaces are frictionless If velocity of sphere is 10x m sec then find x 37 v 16 cm s 2 Consider the situation given in the diagram all surfaces are frictionless If velocity of sphere is 10x m sec then find x 14 37 v 16 cm s

Three blocks A B and C are placed on a roug horizontal surface Friction coefficient between blocks and surface is 0 6 Acceleration of the block C in given situation is g 10 m s 4 kg 6 kg A B C 5 5 kg 1 3 5 m s 3 4 5 m s Three blocks each of mass m are hanges vertically with the help of inextensible strings and 2 0 5 m s 4 Zero

rope which supports A 70 kg man standing on a weighing machine in a 50 kg lift pulls on the the lift as shown in the figure Find the force with which the man should pull the rope to keep the lift stationary Also find the weight of the man as shown by the weighing machine ion Magnitude of tension everywhere in the string is same For equilibrium of the lift

system is at rest Suddenly block P2 is imparted an impulse of 5 N S downwards What is the resulting motion of the system Take mass of p 2kg B P P moves downwards with a constant speed of 5 m s INCORRECT Both P and P2 move downwards with a constant speed of 5 m s

Twinkle throws a stone of mass 1 kg in vertically upward direction It s velocity continuously decreases After attaining a certain height its velocity becomes zero and it starts falling towards earth under gravitational force If the acceleration due to gravity working on it is 10 m sec Then how much force will it exert on ground when it will strike to the ground 1 kg 00 A 10 N B 20 N C 0 1 N D 100 N

A block and sphere are connected by a cord that passes over a pulley as shown Neglect friction and assume the cord is massless Take m m Ma i a What are the magnitude of acceleration in m s2 of the block and sphere m s b What is the tension in N in the cord Enter the magnitude N c What is the speed in m s of each object 2 75 s after being released from rest m s 2 00 kg m d What If If the incline under m is rough what is the minimum value of the coefficient of static friction for which the system will not move H 4 15 kg and 0 51 0

15 16 A force of 4N and another of 9N can be applied together to produce the effect of a single force of A IN C 15 N A 10 m s B 11 N D 20 N Find acceleration of wedge rightwards so that block does not move w r t wedge C 15 m s 53 B 40 3 a m s ALLEN D 25 m m s 15 hich fall uchel ole A IN B 11 N C 15 N D 20 N 16 fanger as an art art aufe A 10 m s C 15 m s 53 B a 40 3 m s If 25 D 2 m m s

Two blocks of mass 2kg and 3kg are placed over each other Coefficient of friction between 2kg and 3kg blocks is 0 8 Ground is perfectly smooth Force of 20N acts on 2kg block as shown in figure Select the CORRECT statement s 0 8 smooth A B 2kg 3kg 20N Friction force between 2kg and 3kg block is 12 N Friction force between 2kg and 3kg block is 16 N C Acceleration of 3kg block is 16 3 m s D Acceleration of 3kg block is 7 m s 5

wwwwwwwwwww Figure 1 Figure 2 www Figure 3 12 Consider three identical massless springs The left ends of the first second and the third springs are affixed to a wall to a block of mass m placed on a horizontal floor not frictionless and to a block of mass m placed on a horizontal frictionless floor respectively as shown in the figures The right end of each spring is pulled by a gradually increasing force When magnitude of the force becomes F extensions in these springs become x x2 and x3 respectively Which of the following state ments is correct x x x c x x x b x X X3 d x x x3

If the force acting on a body is inversely proportional to its speed then its kinetic energy is O Linearly related to time O Inversely proportional to time O Inversely proportional to square of time O Constant

A 20 kg body is pushed with just enough force parallel to surface to start it moving across a floor and the same force continues to act afterwards The coefficient of static and kinetic friction are 0 6 and 0 2 respectively The acceleration of the body is g 10 m s 1 1 m s 3 3 m s 2 2 m s 4 4 m s

5 A particle moving with velocity V is acted by three PQR The velocity forces shown by the vector triangle of the particle will a Increase b Decrease c Remain constant d Ch Q

19 Force acting on a particle of mass m is given by F kv where k is constant and v is velocity If initial velocity is vo the velocity of particle after time t will be 1 v vo kt 3 v v e 1 my k kt e m 4 v v ekt 20 In the previous problem the displacement of particle in terms oft motion starts from origin is kt m 2 v v 1 e vo 2 kt mvo k m kt em

A particle of mass m 3kg is moving on a straight line in a conservative force field in whic the potential energy associated with the particle is given by U y 2y 30y 450 At t 0 particle i at y 8m and moving towards positive y axis with 1 m s A During the course of its motion the maximum speed of the particle will be m s 4 3 B Particle will never cross the origin 5n C Particle will come to its equilibrium position for the first time at second 4 3 D The amplitude of oscillation for the particle is 1m

ABCD is a wire frame of rigid identical wires in which point Dis given velocity v along x axis as shown in figure Choose the correct statemen 4 30 Velocity of point A along x axis is Speed of point A is v NIS Velocity of point A along y axis is 2 Velocity of point A is equal to velocity of point C

7 10 What minimum force F is needed to start body A moving to the right if 25 for all surfaces The following weights are given WAB 100 N W 125 N The length of AB is 2 5 m W SO N 10 60 1 6 m Figure P 7 10

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 the boy can exert on N Round off the rope so that the piece of wood does not move from its place is to the Nearest Integer Take g 10 ms 2 F T R T T Q T

1 6 kg 2 5 m B 2 4 kg 1m 30 s shown in the diagram a particle A of mass 1 6 kg lies on a horizontal plane and a particle B of ass 2 4 kg lies on a plane inclined at an angle of 30 to the horizontal The particles are connected a light inextensible string which passes over a small smooth pulley P fixed at the top of the inclined ane The distance AP is 2 5 m and the distance of B from the bottom of the inclined plane is 1 m here is a barrier at the bottom of the inclined plane preventing any further motion of B The part BF the string is parallel to a line of greatest slope of the inclined plane The particles are released from

Sand from a stationary hopper falls onto a moving conveyor belt at a rate of 5 00 kg s as shown in the figure The conveyor belt is supported by frictionless rollers and moves at a constant speed of 0 750 m s under the action of a constant horizontal external force Fext supplied by the motor that drives the belt y X F ext A The force of friction exerted by the belt on the sand is 3 75 N B The external force F is 3 75 N ext C The work done by F in 1 sec is 2 81 J ext D The kinetic energy acquired by the falling sand each second due to the change in its horizontal motion is 1 41 J

A parachutist whose mass is 85 kg drops from a helicopter hovering 1000 m above the ground and falls toward the ground under the influence of gravity Assume tha the force due to air resistance is proportional to the velocity of the parachutist with the proportionality constant b 20 N sec m when the chute is closed and b 90 N sec m when the chute is open If the chute does not open until the velocity of the parachutist reaches 35 m sec after how many seconds will the parachutist reach the ground Assume that the acceleration due to gravity is 9 81 m sec seconds The parachutist will reach the ground after Round to two decimal places as needed

18 Cords of force constants ka k and kc and relaxed lengths lA IB and lc are joined with each other at one of their ends The free ends of the cords are pulled maintaining them always in a plane For a particular set of pulling forces an arrangement shown in the figure I is obtained and for another set of pulling of forces arrangement shown in the figure II is obtained In the arrangement of figure I extended length of each cord is L and in the arrangement of figure II extended length of each cord is L L KK A 120 120 120 C A 135 90 C Figure I B Figure II B With the help of the given information check validity of the following statements al l lc and k kg kc b lA l lc and either k kg kc or k kB kc c l LB lc if k kg kc or l lg lc if k k kc d l l le if k kg kc or la lg lc if k kB kc B

A van accelerates uniformly down an inclined hill going from rest to 30 m s in 6s During acceleration a toy of mass m 0 1 kg hangs by a light string from the van s ceiling The is such that string remains to the ceiling take g 10m s acceleration perpendicular A

One end of the coil of ideal flexible rope falls through a hole in support table as shown in figure The rope has a length L and mass per unit length 2 Assume the rope to be a conservative continuous inextensible system Which of the following options are correct A the acceleration of the falling rope is equal to g B The acceleration of the falling rope is 2 C The speed of the falling part as a function of the fallen length x is V 2gx 2L D The reaction of the table when x is zero

A pair of scissors is used to cut a wire of circular cross section held vertically To reduce required force the wire must be placed close to the hinge but if it is placed close to the hinge it slides away from the hinge until the angle between the blades becomes 8 Find the coefficient of friction between the blades and the wire a cot 0 50 c 0 5tan 8 tan 0 50 d Insufficient information AP

distance of 1 m on a plane inclined at an angle of 30 with the horizontal Assuming that g 9 81 ms 2 time taken is Question Type Single Correct Type 1 0 32 s 2 0 48 s 3 0 782 s

A block rests on a long plank that is moving with a constant velocity 2 0 s on a horizontal floor Coefficient of friction between the block and the plank is 0 10 If the plank starts decelerating uniformly and stops in 0 50 s what is the distance slid by the block on the plank Acceleration of free fall is 10 m s a 0 50 m c 1 0 m b 0 75 m d 1 5 m 2 0 m s 2 0 m s

Two identical heavy spheres of equal mass are placed on a smooth cup of radius 3r where r is radius of each sphere Then the ratio of reaction force between cup and any sphere to reaction force between two sphere is Question Type Single Correct Type 1 2 1 2 3r3r 3 3

A uniform stick of mass M is placed in a frictionless well The stick makes an angle 0 with the horizontal What is the force in N that the right side of the well exerts on the stick at its end Take M 3 6 kg and q 37 Take g 10 m s M 0

A machine gun fires 180 bullets per minute on a steel plate Each bullet has a mass of 20 g and velocity 1 km s The bullets return with half their velocity after hitting the plate Find the force 30 N necessary to hold the plate so as not to move it

Near a station a train is retarding at 2 0 m s to stop When its speed is 36 km h a passenger standing in the corridor of a bogie puts his suitcase on the floor The floor was a little bit slippery so the suitcase began to slide and finally stopped in the train after sliding 12 m on the floor relative to the train According to this situation which of the following statements are correct The train stopped before the suitcase stopped sliding b Speed of the suitcase relative to the bogie decreases monotonically Speed of the suitcase relative to the bogie first increases then decreases Coefficient of friction between the suitcase and the floor of the bogie is close to 0 135

particle of mass m is moving in a horizontal ciricle of radius R under a centripetal force equal A A constant The total energy of the A particle is Potential energy at very large distance is zero A R 3 A 2R 2 KE T E KE SCAPE VELOCITY A R A 2R

34 A mass is supported on a frictionless horizontal surface It is attached to a string and rotates about a fixed centre at an angular velocity o If the length of the string and angular velocity are doubled the tension in the string which was initially To is now 1 To 3 4T0 2 1 2 2 4 8T0

The wedge is moved towards right with acceleration a which is slowly increased from zero The tension in the string just when the small block of mass m breaks contact with the surface of wedge is Assume al surfaces smooth the string inextensible and neglect rotational effect s m a

A smooth ring A of mass m can slide on a fixed horizontal rod A string tied to the ring passes over a fixed pulley B and carries a block C of mass M 2 m as shown in figure 5 W7 At an instant the string between the ring and the pulley makes an angle 0 with the rod a Show that if the ring slides with a speed v the block descends with speed v cos 0 b With what acceleration will the ring start moving if the system is released from rest with 0 30 ART 0 B

2 4 None of these 5 6 A block of mass 3kg is at rest on a rough inclined plane as shown in the figure below The magnitude of net force exerted by the surface on the block will be g 10m s 1 26N 3kg 30 2 19 5N 3 10N 4 30N

A uniform thick string of length 5m is resting on a horizontal frictionless surface It is pulled by a horizontal force of 5 N from one end The tension in the string at 1 m from the force applied is 1 zero 2 5N 4 IN 3 4N 2

i Lami s theorem is applicable to a Equilibrium of two coplanar concurrent forces b Equilibrium of three Coplanar forces c Equilibrium of three coplanar non concurrent forces d all of the above

Ring A of mass m is in level with top of the smooth pully B when it is suddenly released if h is the distance by which ring moves down a smooth vertical pole before coming to rest for the first time L is the horizontal distance between initial position of ring pulley Find approximately the condition for which ring will slide down even when less in weight than the weight of the block C of mass M A h 4L h 8L C h 2L h 8L B TIT m Tim h B h 4L h 4L D h L 2h 8L

The system shown in figure below consists of two pulleys and two blocks The pulleys each have a mass of 2 0 kg the block on the left has a mass of 16 kg and the block on the right has a mass m If the system is in equilibrium and the string is mass less Determine the mass m in kg 20kg

18kg 30kg 1 2 m s 2 3 m s 4 4 m s 3 3 4 m s2 A person wishes to slide down a rope whose 3 breaking load is of the weight of the person 5 Minimum acceleration by which the person should slide down without breaking the rope is 1 0 8 g 2 1 2 g 3 0 6 g 4 0 4 g A bullet of mass 0 05 kg moving with a speed 4 5