Newton's law of motion Questions and Answers

A bar of 2 m long with negligible weight rests in horizontal position on two smooth inclined planes as shown in Fig Determine the distance x at which the load Q 100N should be placed from point B to keep the bar horizontal P 200N 0 5m 307 2m Q 100N 45 B

A uniform sphere is placed on a smooth horizontal surface and a horizontal force F is applied on it at a dist h above the surface The acceleration of the centre 1 is maximum when h 0 3 is maximum when h 2R 2 is maximum when h R 4 is independent of h

3 14 0 x 10 N 4 1 75 x 10 N Two particles of masses m and m in projectile motion have velocities and i respectively at time t 0 The collide at time to Their velocities become V and V at time 2t while still moving in air The value m m v m m is 1 Zero 2 m m gt 3 2 m m gt 4 m m gt

Mass 1 kg body explodes into three fragments The ratio of their masses is 1 1 3 The fragments of same mass move perpendicular to each other with speeds 30 m s while the heavier part remains in the intial direction The speed of heavier part is 1 10 10 2 m s 3 20 2 m s 4 30 2 m s

A mass of 100g strikes the wall with speed 5m s at an angle as shown in figure and it rebounds If the contact time is 2 x 10 sec what is the force applied on the mass by the wall y 60 250 3 to right Vsie 2 250 N to right bus 100g 60 3 250 3 N to left 4 250 N to left speed

A bullet of mass m and speed v hits a pendulum bob of mass M at time t t and passes completely through the bob The bullet emerges at time t t with a speed of v 2 The pendulum bob is suspended by a light rigid rod of length 7 After the collision the bob can barely swing through a complete vertical circle At time t t3 the bob reaches the highest position What quantities are conserved in this process total kinetic energy of the bob and the bullet during the time interval At t t total momentum of the bob and the bullet during the time interval At t t total mechanical energy of the bob and the bullet during the time interval At t3 t Momentum of the bob after t 1 Save Ne

A block of mass 5 kg is pressed against a wall with a horizontal force of 100 N If the coefficient of friction between the surfaces is 0 8 Then frictional force acting on the block is A D 80 N 50 N 20 N 30 N

A positive charged particle of charge q and mass m is suspended from a point O by a string of length In the space a uniform horizontal electric field E exists The particle is drawn aside so that the string becomes vertical and then it is projected horizontally with velocity v such that the particle starts to move along a circle with same constant speed v A tension in string is mg qE qE B tension in string is mg C kinetic energy of mass is q E 2mg 5 D kinetic energy of mass is mg q E

A block of mass 1kg is placed over a plank of mass 2kg The length of the plank is 2m Coefficient of friction between the block and the plank is 0 5 and the ground over which plank is placed is smooth A constant force F 30N is applied on the plank is hor izontal direction 1 kg The time after which the block will separate from the plank is g 10 m s2 2m 2 kg 2 m F 30 N WALEKS

The position time graph of a body of mass 3 kg is shown in figure The magnitude of impulse acting on the object at t 3 sis 12 m Position 6 m 6 kg m s 9 kg m s 12 kg m s 2 3 t s

A body starts falling from rest from a large height If t 1 and fo are the time taken by the body to cover successive equal distances then 1 is 1 2 3 1 2 3 1 2 4

2 If a ladder is not in balance against a smooth vertical wall then it can be made in balance by A Decreasing the length of ladder B Increasing the length of ladder C Increasing the angle of inclination D Decreasing the angle of inclination

Question48 A student of height h jumps vertically up from the squat position At the top point of the jump the students center of mass is at a height 3h 4 from the ground The average force acting on the floor during the jump prior to the moment when the student loses contact with the floor is F It is known that when the student stands on the floor the center of mass is at a height h 2 from Vedantu YOUR DESCONAL ONULUIE

A sphere of mass 500 g starts moving with an acceleration of 10 m s on application of an impulsive force The force acts on it for 0 5 s Gain in momentum of sphere is 1 2 5 kg m s 3 0 05 kg m s 2 5 kg m s 4 25 kg m s

is 3 9 A bucket containing water of depth 10 cm is kept in a lift which is moving vertically upwards with an acceleration which is equal to 1 times acceleration due to gravity Then pressure intensity at the bottom of the bucket in kg cm 2 is 3 25 10 3 4 25 10 4 O 1 250 2 2500 ol P hd g a 10 x 10 2 X 2500 Nm 2

2 A block of mass M is hanging over a smooth and light pulley through a light string The other end of the string is pulled by a constant force F The kinetic energy of the block increases by 20 J in 1s 1 the tension in the string is Mg 2 the tension in the string is F 3 the work done by the tension on the block is 20 J in the above 1 s 4 the work done by the force of gravity is 20 J in the above 1s Fin distance x If the stopping force is 4F

If a force F is applied Fv 2 F v 3 F v 4 Fv A train weighing 10 N is running on a level track with uniform speed of 36 km h the frictional force is 0 5 kg f per quintal What is the power of the engine g 10 m sec 1 0 5 kw 2 5 kw 3 50 kw 4 500 kw A man is riding on a cycle with velocity 7 2 km hr up a hill having a slope 1 in 20 The total mass of the man and cycle

3 A mass of 6 kg is suspended by a rope of length 2 m as shown in figure A force of 80 N is applied at mid point Pas shown What angle the rope makes with vertical under equilibrium Take g 10 m s 0 1m 80 N

Coefficient of performance B of an ideal refrigerator working between temperatures 7 and T T T is B 11 T T T T T T B T T T T T T

21 A solid cylinder is rolling down on an inclined plane of angle 0 The coefficient of static friction between the plane and cylinder is u then condition for the cylinder not to slip is a tan 023 c tan 0 3 A cylinder is rolling b tan 0 3 d tan 0 3

Q The magnitude of the force in Newtons acting on a body varies with time t in microseconds as shown in fig AB BC and CD are straight line segments The magnitude of the total impulse of the force on the body from t 4 us to t 16 us is N s A B C D 5 x 104 N s 5 x 10 3 N s 5 x 10 5 N S 5 x 10 2 N s Force F N 800 600 400 200 O A 2 B F IE 6 Time us 8 00 10 12 14 D 16

0 i A block of mass 3 kg is pushed against a rough vertical wall of friction coefficient 0 5 by a force F applied at an angle 45 with the vertical and 45 with the normal to the wall Find a the minimum value of F for which the block will remain in equilibrium b the acceleration of the block if the force applied is 2 Fmin found in part a ii If the direction of F can be changed find the minimum value of F required to keep the block at rest by pressing it against the wall

1 Point Total moment of various forces acting on the body is the vector sum of all moments Total moment of various forces acting on the body is the algebraic sum of all moments Total moment of various forces acting on the body is always zero Total moment of various forces acting on the body is the vector sum of all moments which is perpendicular to each other forces

1 The total momentum of a system of masses i e moving bodies in any one direction remains constant unless acted upon by an external force in that direction This statement is called A Newton s first law of motion B Newton s second law of motion C Principle of conservation of energy D Principle of conservation of momentum

3 Greater than W 4 Data is in insufficient A block of mass m lying on a rough horizontal plane is acted upon by a horizontal force P and another force Q inclined at an angle to the vertical The block will remain in equilibrium if the coefficient of friction between and the surface is

1 100 m 2 400 m The minimum force required to start pushing a body up a rough frictional coefficient u inclined plane is F while the minimum force needed to prevent it from sliding down is F If the inclined plane makes an angle from AIEEE 2011 the horizontal such that tan 0 2u then the ratio F F 1 I 2 2 3 3 is 4 4 Main I NEET AIIMS 29

1 3 2F ELE m 3 Zero F 2m 0000000 m vovovor 4 Which among the following is correct for conservative forces Work done by a conservative force in a closed path is 1 Positive 2 Zero 3 Negative 4 All of these are possible 10 A spring of spring constant k is compressed by an amount of x and a mass m is just placed in contact with it and released Calculate minimum value of x for which the mass m completes the vertical circle in the circular track 1 2gR m m Natural length position F 2 smooth 5gR m k 2 3 5gR 4 None of these k Two blocks in contact with each other are being pushed by a external agent as shown 1 3 14 m F m m 3 m m m 12 A particle of mass m is moving in a circular path o fixed radius r such that its centripetal acceleration 1 Vo 3 a is varying with time as a k rt2 where ki constant The power delivered to the particle by th forces acting on it as a function of time t is 1 2 mk r t 2 mk r t mk4r215 Fv 1 Zero 2 Fv projection with speed resistance is 4 13 A body of mass 0 5 kg travels in a straight line w 3mv 4 1 velocity v ax3 2 where a 5 m 2 s The w done by the net force during its displacement fr x 0 to x 2 m is 2 50 J 1 1 5 J 3 10 J 4 100 J A body of mass m is projected vertically wi velocity vo If it passes through the poir m F m m 4 O Vo 1 2 the work done b 2 Foror 15 A massless spring when stretched by a force shows an extension of 1 5m This sp arranged as shown in figure A block of mas is released at rest on a frictionless incline down and compresses the spring by 3m coming to rest momentarily Distance by wi block slides before hitting the spring is 0 30 3mv 4 3mv 8 10Kg

0 Can a dimensionless quantity have a unit Define Impulse of a force How is it related to momentum A 30 g bullet leaves a rifle with a velocity of 300 m s and the rifle recoils with a velocity of 60 c Find the mass of the rifle 3 1 2

A block of mass 0 2 kg is suspended from the ceiling by a light string A second block of mass 0 3 kg is suspended from first block through another string The ratio of tension in two strings is 2 3 3 2 O 1 2 O 5 3

Find accel Acceleration of free fall is g 7 An arrangement setup inside a lift is shown in the figure The pulleys and threads are ideal and masses of the blocks are m and M M 2m Find minimum acceleration of the lift for which the thread remains taut and both the blocks accelerate in the same direction relative to the ground Acceleration due to gravity is g are of equal mass the m M

Two bodies M and M are connected by a light string passing over a light smooth pulley at the end of an incline The mass M lies on incline and mass M hangs vertically The system is at rest M Calculate the angle of incline and the force exerted by the incline on the body of mass M

A ball of mass 1 kg collides perpendicularly on a smooth stationary wedge of mass 2 kg kept on a smooth horizontal surface The coefficient restitution is e 1 2 The velocity of ball after the collision is m s The value of K is ma V 10 m s 0 30 M

3 tan 1 4 4 tan 2 38 A man moves on a horizontal road towards east at a speed of 1 km h and the rain appears to him falling vertically at a speed of 2 km h The actual speed of the rain is 1 1 km h 3 3 km h 2 2 km h 4 5 km h and its

A uniform rod AB of length L 2 3 m and weight W 124 N acting through the centre of the rod is supported by two vertical strings at its ends Suspended from the rod at a distance of x 0 77 m from A is a load of m 21 kg as shown in the diagram below Determine the tension in the string connected at B A m L W B Take the acceleration due to gravity as a 9 8

The coefficients of friction and masses of various blocks are shown If f is the limiting frictional force between block A and surface and f is the frictional force between block B and C for what value of applied force F f 5f 71 B 10 57 10 A C 51 10 mg 61 10 umg D mg umg B mass 10 m Rod 09 8 C mass 50m P 0 A mass m f ELE

In the figure shown a block of weight 10 N resting on a horizontal surface The coefficient of static friction between the block and the surface 0 4 A force of 3 5 N will keep the block in uniform motion once it has been set in motion A horizontal force of 3N is applied to the block then the block will Choose only 1 answer A R Your Answer Move over the surface with constant velocity Move having accelerated motion over the

1 To determine the coefficient of friction between a rough surface and a block the surface is kept inclined at 45 and the block is released from rest The block takes a time t in moving a distance d The rough surface is then replaced by a smooth surface and the same experiment is repeated The block now takes a time t 2 in moving down the same distance d The coefficient of friction is WB JEE 2014

2 A block of mass M sits on an inclined plane and is connected via a massless string through a massless pulley A that slides without friction on the plane to a fixed post This pulley is in turn connected via a massless string through a second massless pulley B to a second block of mass 2M that hangs above the ground The coefficient of static friction between the inclined plane and block resting on the inclined plane is The inclined plane is tilted to an angle 0 w r t horizontal so the blocks just start to move Find the value of the quantity 3 cos 0 sin 0 2M 0

ofv A ball of mass m moving horizontally which velocity u hits a wedge of mass M The wedge is situated on a smooth horizontal source If after striking with wedge the ball starts moving in vertical direction and the wedge starts moving in horizontal plane Calculate a the velocity of wedge V b the velocity v with which the ball moves in vertical direction the impulse imparted by the ball to the wedge d the coefficient of restitution e 0 m

SINGLE OPTION CORRECT TYPE When forces F F2 and F3 are acting on a particle of mass m such that F2 and F3 are mutually perpendicula hen the particle remains stationary If the force F is now removed then the acceleration of the particle is AIEEE 20 F F3 m A Flm B F2F3 mF1 C D F2lm the

Example 16 Two identical billiard balls strike a rigid wall with the same speed but at different angles and get ref lected without any loss of speed as shown in Fig 5 19 What is i the direction of the force of the wall due to each ball and ii the ratio of the magnitudes of the impulses imparted on the two balls by the wall NCERT Delhi 161

D All the above When the branch of a tree is shaken the ripe fruits get detached from the branch This is ar example of A Newton s first law of motion C Newton s third law of motion B Newton s second law of motion D All of the above

Find out the acceleration of the block B in the following systems B 4 a 2m b B 3m

A man of mass m climbs on a rope of length L suspended below a balloon of mass M The balloon is stationary with respect to ground If the man begins to climb up the rope at a speed Vrel relative to rope In what direction and with what speed relative to ground will the balloon move A downwards B upwards C downwards mvrel m M mvrel M MV rel m M D downwards M m V rel M direction At the highest

A light rope fixed at one end of a wooden clamp on the ground passes over a tree branch and hangs on the other side figure 5 W9 It makes an angle of 30 with the ground A man weighing 60 kg wants to climb up the rope The wooden clamp can come out of the ground if

A mercury thermometer is placed in a gravity free hall without touching anything As temperature rises mercury expands and ascend in thermometer If height ascend by mercury in thermometer is h then by what height centre of mass of mercury and thermometer system descend

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At the instant shown in the figure the block A is moving downwards at speed u If the string is tight and the block B moves horizontally the speed of block B is Options B O 20 cose Au towards right Xucos towards right 21 towards right sin e

A 4g bullet is fired horizontally with a speed of 300 m s in to 0 8 kg block of wood at rest on a table If the coefficient of friction between the block and the table is 0 3 how far will the block slide approximately 2014 A 0 19 m C 0 569 m B 0 379 m D 0 758 m rough horizontal floor To do so person A pushes it at an

Q18 At the instant shown in the figure the block A is moving downwards at speed u If the string is tight and the block B moves horizontally the speed of block B is www w Options X B 20 cose Au towards right ucose towards right 11 towards right sin e