Newton's law of motion Questions and Answers

A block is placed on a rough horizontal surface A time dependent horizontal force F kt acts on th block whero k is positive constant Acceleration time graph of the block is Haryana NTSE Stage 1 2014 A B 2 C D

1 2 mg 2 mg 3 3 mg 4 10 mg 33 A cart loaded with water having total mass m 1000 kg moves on a straight horizontal road starting from rest under the action of a force of 100 N The water spills through a small hole in the bottom at a rate of 0 1 kg s The velocity of cart after 300 s is 36 A par wedg figur min is Fzmati Vb dt 1 11 m s 2 21 m s 3 31 m s 4 41 m s 4 Two blocks of masses 1 kg and 0 75 kg are

A block rests on a horizontal surface and a man pulls it with a 10N force Rank the situation show below according to the magnitude of the normal force exerted by the surface on the block least maximum 1 ION 10N ION 3

3 p dt dt 76 An sphere weighs 10 N and rest in V shaped trough whose sides form an angle 30 Normal reaction excerted by wall B on sphere is 1 10 N 3 5 N 30 CON B A 2 5 3 N 4 Zero 150 10 100 25 81 A partic in equil angle F ap 10 2 3 4 82 A b stri

Calculate the tension in the rope of mass M length L at the given point P as shown in the figure X M 1 mg xg 3 mg Mg m M L Tp M 2 mg L x g L 4 Zem

O A heavy box is to be dragged along a rough horizontal floor To do so person A pushes it at an angle 30 from the horizontal and requires a minimum force FA while person B pulls the box at an angle 60 from the horizontal and needs minimum force FB If the coefficient of friction between 3 FA is the ratio FB the box and the floor is F cose 3 mg Fasing 5 5 1 3 3 312 1 2 4 3 2 3 Fb cos 0 3 mg Fosing 5 2014 Fa cose Msingi mg F 2050 Msin 0 mg

In the system shown initially the block A of mass m is hanging at rest and the block B of mass 2m is on the ground The pulleys have negligible masses and negligible friction and the thread is extremely light and almost inextensible Acceleration due to gravity is g The free end of the thread is pulled upwards with a constant force When it acquires a speed u find speeds of both the blocks B

A block of mass 1 kg is placed on a rough wedge which is fixed on an elevator moving upward with constant velocity 2 m s The block m is at rest w r t wedge Net reaction force on the block is 11 1 5 N 2 75 N 3 2 30 m 2 m s 2 10 N 4 12 N C

An iron block of mass m 500 kg is kept at the back of a truck moving at a speed Vo 90 km h The driver applies the brakes and slows down to a speed of v 54 km hr in 10 s What constant force acts on the block during this time if the block does not slide on the truck bed

In the JWH in figure pulleys A and B are massles and frictionless and threads are ideal Block of mass m will remain at rest if 1 1 m3 4 m 2 3 m M 1 1 A B m m 2 m m m 1 1 1

3 Thoro are two forcos on the 2 0 kg box in the overhoad vlow of figuro but only ono is shown Tho socond forco is noarly A 20 N 30 F 20 N a 12 mus B 201 20 N C 321 123 N 0 211 16 N

371 Two blocks 4 kg and 2 kg are sliding down an incline plane as shown in the figure The acceleration of 2 kg block is a 1 66 m s 2 2 b 2 66 m s c 3 66 m s 2 12 0 3 4 kg 30 0 2 2 kg Fig 4 78

A light inextensible string of length 15 m is hanging between two pegs that are 9 m horizontally apart as shown A small frictionless pulley of weight W 4 8 N supporting a block of weight W 8 0 N is gently placed on the string and allowed to move gradually to a place on the string where it can stay in equilibrium Radius of the pulley wheel is negligible as compared to the length of the string Which of the following conclusions can you make when the pulley is in equilibrium a Level difference of the pegs is 4 0 m b Tensile force in the string depends on the level difference of the pegs e Tensile force in the string is 8 0 N irrespective of the level difference of the pegs d Lengths of string segments on left and right sides of the pulley are 10 m and 5 0 m respectively Newton s Laws of Motion 25 Pulley suppor ting the block

All pulleys are smooth and light Pulley E is fixed but pulleys C and D are free to move Find the acceleration of blocks A and B a aA g ag 0 40 m A E 2m B b a 0 ag 0

In figure shown both blocks are released from rest The time to cross each other 2 second B 3 second 2m 4 kg 1 kg 4m C 1 second D 4 second

24 Grains of fine California beach sand are approximately spheres with an average radius of 50 m and are made of silicon dioxide which has a density of 2600 kg m What mass of sand grains would have a total surface area the total area of all the individual spheres equal to the surface area of a cube 1 00 m on an edge

Two blocks A and B with mass 4 kg and 6 kg respectively are connected by a stretched spring of negligible mass as in figure When the two blocks are released simultaneously the initial acceleration of B is 1 5 mi s westward The acceleration of A is M 0 92 1 1 m s2 westward 3 1 m s2 eastward 1 5m s Awwww B Smooth 2 2 25 m s2 eastward 4 2 75 m s2 westward A body of mass 32 kg is suspended by a spring balance from the roof of a vertically operating lift and going the lift has covered 20 m and 50 m the spring balance showed 30 kg

For the system shown in the figure the acceleration of the mass m immediately after the lower thread x is cut will be assume that the threads are weightless and inextensible the spring are weightless the mass of pulley is negligible and there is no friction CALO m m B m m m m

A moving block having mass m collides with another stationary block having mass 4m The lighter block comes to rest after collision When the initial velocity of the lighter block is v then the value of coefficient of restitution e will be NEET 2018 1 0 5 2 0 25 3 0 4 4 0 8

of 4 kg is suspended as shown in figure with the help of massless inextensible string A Another identical string B is connected at the lower end of the block When a sudden pulling downward jerk slightly greater than breaking strength of A and B is given to string B then A 1 Roth 4 kg B 1 String A will break 2 String B will break 3 Both A and B will break simultaneously

5 Two weights w and we are connected by a light thread which passes over a light smooth pulley If the pulley is raised upwards with an acceleration equal to g then the tension in the thread will be A 2w W2 W W2 B W W 2 W W2 C 4W W2 W W D 4W W2 W W2

nd is assuming y axis is NCERT pg 78 ST with speed 5 m s h the ground The e fourth of height INCERT pg 79 1 5 km h 2 5 2 km h 3 10 km h 4 4 km h 14 The angle of projection of a projectile which is T projected with certain velocity from ground is 8 horizontal and its horizontal range is R The angle with the horizontal for another projectile having same range R and speed is NCERT pg 78 1 3 3 8 T 2 R 4 with T

6 21 4 M M 2 4M M A man of mass m stands on a platform of equal mass m and pulls himself by two ropes passing over pulleys as shown If he pulls each rope with a force equal to half his weight his upward acceleration would be downward 1 1 g 2 4M M 2 g 4 M 4M 3 g 4 zero

11 5 1 Zero Three rings each of mass m and radius rare the system about the axis as shown in the figure is side is A uniform rope of length L and mass M is placed on a smooth fixed wedge as shown Both ends of rope at same horizontal level The rope is initially released from rest then the magnitude of initial acceleration rope is M a 2 cosa cos g 3 tana tan g pla EIN VIN 4 coseca cosec g arated by a 3 of a light orizontal

6 13 A body of mass 3 kg hits a wall at an angle of 60 and with speed of 10 m s and returns at the same angle The impact time is 0 2 sec Calculate force exerted on the wall 1 150 5 2 100 N 60 60 10m s 2 50 5 75

Two particles of mass m each are tied at the ends of a light string of length 2a The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance a from the centre P as shown in the figure Now the mid point of the string is pulled vertically upwards with a small but constant force F As a result the particles move towards each other on the surface The magnitude of acceleration when the separation between them becomes 2x is F a 1 2m y A F X 2m m EO 2 F P 3 EO m FX 2m a F 2m X

A perfectly straight portion of a uniform rope has mass M and length L At end A of the segment the tension in the rope is T and at end B it is T TB TA Neglect effect of gravity and no contact force acts on the rope in between points A and B The tension in the rope at a distance

In the two cases shown below the coefficient of kinetic friction between the block and the surface is the same and both the blocks are moving with the same uniform speed Then F F A F F 8 F F C F F D F 2F if sino Mg F

System shown in the figure is released from rest when spring is unstretched Pulley and spring is massless and friction is absent everywhere The speed of 5 kg block when 2 kg block leaves the contact with ground is Take force constant of spring k 40 N m and g 10 m s A 2 m s Assume the aerodunor B 2 2 m s 5 kg 2 kg TTTTTTT C 2 m s P 4 2 m s

A metallic block of mass 2 kg is placed on the horizontal surface The block is going to slide down as the plane surface is inclined at an angle of 15 Calculate the coefficient of friction between the surface and the block a Mg sin 0 R Mg FS Mg cos B

14 A block of mass 4 kg is suspended through two light spring balances A and B in series Then A and B will read respectively 3 zero kg and 4 kg 4 2 kg and 2 kg onnected with a light string are placed over a frictionless pulley This set 1 4 kg and zero kg 2 4 kg and 4 kg JZYAK

Mass m placed on a plank of mass m lying on a smooth horizontal plane A horizontal force F at a is a constant is applied to a bar If acceleration of the plank and bar are a and a respectively and the coefficient of friction between m and m is u Then find acceleration a with time t F

3 The vertical displacement of block A in meter is given by y 12 4 where t is in second The downward acceleration a of block B in m s is 3 10 4 5

64 A particle of mass m moves in a circular radius 2m with a speed of 10m s Calculate time after which the magnitude of change in moment momentum becomes equal to its initial T 1 sec 15 T 5 3 sec 1 2 2 2 sec 2 4 Not possible 65 A body starts moving in a straight line under th influence of a variable force F Calculate the time after which the initial velocity of body becomes equal to the final velocity of body for the giver F t graph F in N A 2 15 sec t sec 2 2 2 sec is 30 The graph of the frictional fo plane with 0 is 1 3 30

275 A block of mass m lies on a smooth horizontal table and is connected to another freely hanging block of mass m by a light inextensible string passing over a smooth fixed pulley situated at the edge of the table Initially the system is at rest with m a distance d from the pulley Then the time taken for m to reach the pulley is 1 3 m m g m m 2m d m m g d 2 m 2d m m m g 4 None of these

Two particles of masses m and m in projectile motion have velocities V and V respectively at time t 0 They collide at time to Their velocities become v and v2 at time 2to while still moving in air The value of mv m v m v m v is A zero B m m gto C 2 m m gto 2 1 21 D m m gto 2001

An automobile spring extends 0 2 m for 5000 N load The ratio of potential energy stored in this spring when it has been compressed by 0 2 m to the potential energy stored in a 10 F capacitor at a potential difference of 10000 V will be A 1 4 B 1 C 1 2 D 2

In Fig 8 271 the ball A is released from rest when the spring is at its natural unstretched length For the block B of mass M to leave contact with ground at some stage the minimum mass of A must be a 2M c M 2 eeeeee BM Fig 8 271 b M d M 4

B A particle of mass m comes down on a smooth inclined plane from point B at a height of h from rest The magni tude of change in momentum of the particle between position A just before arriving on horizontal surface and C assuming the angle of inclination of the plane as with respect to the horizon tal is a 0 2m ah sin 0 C 771 Fig 1 238 b 2m 2gh sin 8 d 2m 2h

52 A particle of mass 1 kg is suspended from a ceiling through a string of length 10 2 m The particle moves in a horizontal circle Find its time period 1 r 45 TC

M m Figure 6 E10 28 Find the acceleration of the block of mass M in the situation of figure 6 E10 The coefficient of friction between the two blocks is u and that between the bigger block and the ground is

An open vessel containing water is given a constant horizontal acceleration a Due to accelerated motion the free surface of water makes angle 8 with veritcal which is given by e tan 3 0 sin a g a 2 0 tan 9 9 a 4 0 cos 96

A horizontal force F 2 N is applied on the system shown in the figure All surfaces are smooth All pulleys and string are ideal Mass of A and B each is 1 kg What is the acceleration of B with respect to A FE 1 1 m s 3 2 m s A 2 4 m s 4 Zero

A force F acts on a smooth block of mass m placed on a horizontal floor at an angle 0 with horizontal On the block A the net force F cos 0 if F sin 0 mg F cose B acceleration when F mg cos ec e acceleration F m if F sine mg m D N mg Fsin 0 if Fsin0 mg a t m Fsimo ing

Consider the situation shown in the figure given below All the surfaces are frictionless and the string and the pulley are light Find a The accelerations of the two blocks b The tension in the string my a m

A 10 kg block kept on an inclined plane is pulled by a string applying 200 N force A 10 N force is also applied on 10 kg block as shown in figure Find net force on pulley exerted by string A 200 N B 100 2 N C 200 2 N D 200 3 N 10N 30 60

A spaceship is moving 9 8 m s 2 in a fixed direction in space where attrac tion due to other planets and stars is negligible Find the magnitude and direction of the force exerted by a body of 98 N in the spaceship Ans 98 N opposite to the direction of motion of the ship

1 3 mg 3 mg 5 2 Smooth 5 kg 1 22 5 N 3 90 N 2 3 kg 4 NIC 2 s Two blocks of masses 8 kg and 5 kg are connected with a rod of mass 3 kg The 8 kg mass is pulled with force of 180 N The tension in rod at contact point of 8 kg block is mg mg 2 8 kg F 180 N 2 45 N 4 180 N

of a body is given by the equation a 4 3v m s2 Speed v is in m s and t is in second If initial velocity is zero then terminal velocity of the body is 23 Acceleration 1 m s 3 3 3 4 m s 2 4 m s 4 Infinite

2 A bead of mass m is released from rest at A to move along the fixed smooth circular track as shown in Fig 8 260 The ratio of magnitudes of centripetal force and normal reaction by the track on the bead at any point Po described by the angle 0 0 would A9 Po a Increase with 0 b Decrease with 0 c Remain constant R Fig 8 260 h O decrease