Newton's law of motion Questions and Answers

0 Block A of mass 6 kg and block X are attached to a rope which passes over a pulley A force P 50 N is applied horizontally to block A keeping it in contact with a rough vertical face The coefficients of static and kinetic friction are s 0 40 and 0 30 The pulley is light MK and frictionless In figure the mass of block X is set so that block A is on the verge of slipping upward The mass of block X is o kg Fill the value of a in OMR sheet rough 0 40 M 0 303 A X P

Two blocks of masses 8kg and 4 kg respectively are connected by a string as shown Calculate their accelerations if they are initially at rest on the floor after a force of 100N is applied on the pulley in the upward direction g 10 m s

In the shown diagram particles A and B are of mass 10 kg and 8 kg respectively and rest on planes They are connected by a light inextensible string passing over a smooth fixed pulley at C Assume all surfaces are frictionless The acceleration in m s of the system is p The value of A C OB 45 9 10 is

A painter of mass M stands on a platform of mass m and pulls himself up by two ropes w over pulley as shown He pulls each rope with force F and moves upward with a uniform tion a Find a neglecting the fact that no one could do this for long time 1 3 4F M m g M m F M m g M m 2 4 2F M m g M m 4F M m g M m

Three particles are projected In air for maximum range such that the first goes from A to B the secon goes from B to C and the third goes from C to A Points A and C are at the same horizontal level The two inclines make the same angle a with the horizontal as shown Then the relation among the projection speeds of the three particles is A U U U B1 2014 12 C 1 1 113 11 11 D u u u U B U U3

The average acceleration of a particle performing simple harmonic motion over one complete oscillation is 1 A 3 Zero 2 4 2 00 A

7 A car starts from rest initially moves with constant acceleration 3 m sec and after some time it moves with constant retardation 2 m sec and total time of journey is 10 sec then find total distance travelled by car 1 40 m 2 60 m 3 80 m 4 100 m

32 A uniform hollow cylinder of mass m rests on a wedge of mass M that is held on a frictionless slope of inclination as shown in the figure Friction between the cylinder and the top horizontal surface of the wedge is sufficient to prevent sliding of the cylinder after the wedge is released Find acceleration of the wedge after it is released

Two blocks A and B of masses 10 kg and 20 kg respectively are kept on rough horizontal surface 0 1 for each block and a horizontal force of 200 N is applied on B as shown in the figure If at some instant 10 kg mass has an acceleration of 10 m s 2 then what is acceleration of B 2 A 10 ms K mmmmm 10 2 5ms 3 5ms 2 5ms 2 4 5 m s B 20 F 200 N

In the given figure pulley is frictionless and string in inextensible g 10 m s Column I A Force by 3 kg on 2 kg B Force by 3 kg on pan C Tension in string D Net force on 10 kg block P 200 3 N Q 100 3 R 80 3 N S 20 N 10 kg B Massless pan Column II 2 kg 3 kg

141 In the figure all pulleys P1 P2 P3 are massless and all the blocks 1 2 3 are identical each having mass m The system consist of infinite number of pulleys and blocks Strings are light and inextensible and horizontal surfaces are smooth Pulley P1 is moved to left with a constant acceleration of ao Find the acceleration of block1 Assume the strings to remain horizontal O ao P1 O TUTTTTTT P2 7 2 P3 O 3

2 The particle is given by x a a t a t The acceleration of the particle is AS HAAR 244 24 x ao a t azt EaRL u Hi vua 34 H NG 42 1 ao 2 9 3 a 4 2a2 A particle has velocity given by v 20 0 1 t2 then it has v 20 0 1t sp eil uld 22 1 uniform acceleration 2 uniform retardation 3 non uniform acceleration 4 zero acceleration 1 218 2 Gua

als he py nd 13 cm iii A vessel full of water has a bottom of area 20 cm top of area 20 cm height 20 cm and volume half a litre as shown in figure 7 16 a Find the force exerted by the water on the bottom 20 cm Figure 7 16 20 cm

system 4 neither the linear momentum nor the kinetic energy of the system 66 A small sphere is moving at a constant speed in a vertical circle Below is a list of quantities that could be used to describe some aspect of the motion of the sphere I I I kinetic energy II gravitational potential energy III momentum Which of these quantities will change as this sphere moves around the circle 1 1 1 I and II only 3 III only com 2 I and III only 4 II and III only 4 f 06 B a nici aziuz qa faxx n nfa aux co fe fer 30 n 1 g 1 3 II Terita fufaa zi III H 1 3 Space for Rough Work kada am d m 111 III 2 11 4 11 af L S Macam M n acom 1

A ball is dropped vertically from a height d above the ground It hits the ground and bounces up vertically to a height d 2 Neglecting subsequent motion and air resistance its velocity v varies with the height h above the ground as IIT 2000 A C B D d h

1 A cylinder of height 20 m is completely filled with water The velocity of efflux of water in m s through a small hole on the side wall of the cylinder near its bottom is 1 10 2 20 3 5 4 25 2 An AC supply has RMS voltage 30 V which is fed in a pure resistance of 10 2 The average power dissipated in this is 1 99 watt 2 45 watt 4 90 watt 3 180 watt A proton a deuteron and an alpha particle with same kinetic energy enter in a region of uniform magnetic field moving at right angles to magnetic field What is the ratio of radii of their circular paths 1 1 2 1 2 1 2 2 3 2 1 1 4 2 2 1 A block takes twice as much time to slide down a 45 rough inclined plane as it takes to slide down a similar smooth plane The coefficient of friction is 3 4 jedical IIT 5 6 314 3 3 2 N 3 4 114 Find the amount of work done to increase the temperature of one mole of an ideal gas by 60 C if it is expanding under the condition V 723 R 8 31 mol K 113 1 166 2 J 2 332 4 J 3 448 6 J 4 216 2 J A body is dropped from height 10 m After striking the surface it rises to 8 m what is fractional loss in kinetic energy during impact Assuming no air resistance 15 314

54 A uniform sphere is placed on a smooth horizontal surface and a horizontal force F is applied on it at a distance h above the surface The acceleration of the centre A is maximum when h 0 B is maximum when h R C is maximum when h 2R D is independent of h 00101100

Two blocks A and B of masses 2m and m respectively are connected by a massless and inextensible string The whole system is suspended by a massless spring as shown in the figure The magnitudes of acceleration of A and B immediately after the string is cut are respectively 9 29 10 O9 2 3 9 9 99 B 2m E

A particle of mass m is dropped from a height h above the ground At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of 2gh If they collide head on completely inelastically the time taken for the combined mass to reach the ground in units of e 12 LM1 2 IN

lise D a 0 and a 4 m s right A block is hanging by a rope in a lift and lift is accelerating upward This motion is observes by two obse A B Here observer A is in lift observer B is at rest on ground then n Lift m observer A observer B A Tension in rope is same with respect to observer A and observer B B Tension in rope is m g a w r t observer B tension is Mg w r t observer A C Tension is rope is M g a w r t observer B zero w r t observer A O Net force on the block is zero w r t observer A

3 3 120 V 4 30 V Block A and B is connected with string as shown in the figure Coefficient of kinetic friction between 1 block A of mass 4 kg and fixed inclined plane is 2 If the block A is moving up the plane with constant speed then mass of block B is approximately 4 4kg 30 B 1 5

and 1 A cable that can support a load of 800N is cut int two equal parts The maximum load that can b supported by either part is 1 100N 3 800N 2 400N 4 1600N

Figure shows a uniform disc with mass M 2 4kg and radius R 20cm mounted on a fixed horizontal axle A block of mass m 1 2kg hangs from a massless cord which is wrapped around the rim of the disc The tension in the cord is A 12 N B 20 N C 24 N

mo m 30 In the arrangement shown masses of blocks are mo 5 kg m 5 k and m 10 kg and radius of the movable pulley is r 10 cm Th threads and the pulleys are ideal and friction between the blocks an the horizontal surface is negligible Find change in angular velocity c the movable pulley in a time interval At 0 22 s Acceleration of free fal is g 10 m s

Spring scale is attached to the ceiling and to them we suspended load of mass m 150 kg Under the weight a man stands on massless platform connected to weighing machine The weight of man is P 70 kg What would be the reading of balances if the man exerts a force P 350 N on the hanging load in downward direction 1850 N in scale A 500 N in scale A 350 N in scale B ON in scale B

Two boys are standing on a frictionless surface Ram mass 80 kg pushes Shyam mass 50 kg Shyam exerts same force on Ram as exerted by Ram on him The centre of mass of both boys remains at rest Ram remains at rest but Shyam accelerates After some time Shyam has moved more distance than Ram

A car moving with a velocity of 10 ms 1 can be stopped by the application of a constant force F in a distance of 20 m If the velocity of the car is 30 ms it can be stopped by this force in M 9 b 20 m c 60 m 2 d 180 m a 20 3 m

19 KE acquired by a mass m in travelling a certai distance d starting from rest under the action of a constant force F is 1 Directly proportional to m 2 Directly proportional to m 3 Directly proportional to 4 None of these E 1

5 For average velocity to be equal to initial and final velocities A must be constant C can be anything the acceleration for linear motion Where V and V is th B may be constant or variable but it is not possible for all possible motion D can t comment

A particle has a velocity u towards east at t 0 Its acceleration is towards west and is constant Let XA and XB be the magnitude of displacements in the first 10 seconds and the next 10 seconds B C D XA XB XA XB XA XB the information is insufficient to decide the relation of XA with XB X 6 Correct MY PE SC

4 The displacement of a body is given by 2s gt2 where g is a constant The velocity of the body at any time t is A gt skipped B C gt 2 gt 2

Two ident springs of spring constant 1000 N m are connected by an ideal pulley as shown and system is arranged in vertical plane At equilibrium 0 is 60 and masses m and m are 2 kg and 3 kg respectively The elongation in each spring when 0 is 60 is p cm The value of reeeee m m eeeeeee 3p 1 6 is

The elevator E shown in figure move downward with a constant velocity 15 ft s The relative velocity of the cable with respect to the elevator is C M 1 30 ft sec 3 15 ft sec E W 2 45 ft sec 4 60 ft sec

2 A block X of mass m strikes another block Y of mass 2m Both the blocks collide and at point of collision the block X exerts the force of 10 N to block Y What will be the size and direction of the force exerted by block Y a 10 N in the same direction of force of block X b 20 N in the same direction of force of block X c 10 N opposite to the direction of force of block X d 20 N opposite to the direction of force of block X

Suppose a rope is tied tightly between two trees that are 30 m apart You grab the middle of the rope and pull on it perpendicular to the line between the trees with as much force as you can Assume this force is 1000N and the point where you are pulling on the rope is h 1m from the line joining the trees What is the magnitude of the force tending to pull trees together 1 2500 N 2 5000 N 3 7500 N 4 10000 N

20 Average speed of a particle for a time duration may be 1 Zero 3 Negative In the following questions 2 Positive 4 Both 1 and 2 21 to 23 a statement of

A person holds the rope assumed massless that passes over a pulley The person is balanced by a block of mass m hanging at the other end of the rope Initially both the person and block are motionless The person then starts climbing the rope by pulling on it with a constant force in order to reach the block The person moves a distance L relative to the rope Friction is absent between rope pulley By how much distance does the block move

Two blocks A and B are connected by an ideal spring passing over a smooth light pulley as shown in the figure Tension in the string connected with block A will be 5 kg A O100 N O 50 N O 25 N B5 kg 70 N

Question 26 A stone of mass m tied to the end of a string revolves in a vertical circle of radius R The net forces at the lowest and highest points of the circle directed vertically downwards are choose the correct alternative Lowest point Highest point a mg T mg T b mg T mg T2 c mg T mv R mg T mv R d mg T mv R mg T mv R Here T T and v v denote the tension in the string and the speed of the stone at the lowest and the highest point respectively

3 A particle of mass m starts moving from origin along x axis and its velocity varies with position x as v k x The work done by force acting on it during first t seconds is 1 3 mk4t 4 mk4t 8 2 4 mk t 2 mk t 4

n Drops of water each of radius 2 mm falls through air at a terminal velocity of 4 m s If they coalesce to form a single drop then terminal velocity of combine droplet is 16 m s The value of n is 02 04 06 O 8

A bus is moving with a speed of 10 ms 1 on a straight road A scooterist wishes to overtake the bus in 100 s If the bus is at a distance of 1 km from the scooterist with what speed should the scooterist chase the bus AIPMT Prelims 2009 1 40 ms 2 25 ms 1 3 10 ms 1 20 ms 1

A string S is connected to weights of mass M and m Forces F and fare applied to the masses Now match the entries in Column I to those in Column II Assume surface to be smooth mmmm F ColumnI A F 20N F 10N M 10kg m 10gram B F 10N f 20N M 10kg m 10gram C m M F 20N F 10N D F f M 10kg m 10gram Column II p tension in the string approximately 20 N q tension in the string approximately 10 N r acceleration is zero s tension in the string is independent of mass t acceleration is not zero A q t Bp t Cs t D s r A 9 1 B p C s Dr A q B t C t D s

Bucke its is being suspended on two weightless springs in two different configurations In the first case the springs are connected to bucket in parallel and exert restoring forces of 20 N and 30 N respectively configuration pictured on the left Find ratio of forces the springs will exert when the same bucket is suspended in series configuration with same two springs shown to the right www 20N 30N

1 You pour a quantity of flour of volume V 225 cm onto a board where it forms a conical pile The coefficient of static friction between flour grains is H 1 60 Find the maximum height in cm of the pile Take 3 15

56 particle moving along X axis varies with its position x as shown in figure The acceleration a of particle varies with position x as v ms 1 vaz xx 10 Do 0 a a x 3 c 2a 3x 5 dn G V d 2 al W x m b a 2x 4 a 4x 8 NN N 30 bath itu 30 km

If block is sliding down on a rough plane with constant velocity as shown in the figure then net force acting on the wedge due to block is 1 mg Cos 0 3 mgcose m N 0 2 mg 4 None of these

1 A block of mass 4 kg is suspended through two light spring balances A and B Then A and B will read respectively 4 kg 1 4 kg and zero kg 3 4 kg and 4 kg 2 zero kg and 4 kg 4 2 kg and 2 kg

4 40 N down the plane 45 For figure calculate the angle 0 and the tension in the rope AB if M 300 kg and M 400 kg Assuming system is in equilibrium 10 30 1 53 4000N 3 37 4000N B M M 2 53 5000N 4 37 3000N

When a force Facts on a particle of mass m the acceleration of particle becomes a Now if two forces of magnitude 3F and 4F acts on the particle simultaneously as shown in figure then the acceleration of the particle is 1 a 3 5a 4F 90 m 3F 2 2a 4 8a