Newton's law of motion Questions and Answers

A disc which is at rest started to spin about a stationary axis The angular acceleration of the disc is given by a 20 rad s where is the angle of rotation of disc from its Initial position Which of the following graphs correctly represents the variation of angular velocity with respect to 0 w rad s A B OC D co rad s w rad s w rad s V Solution B w K Given a 20 We know a dw do wdw 20d0 1 20 w dw dt 0 rad 9 rad 0 rad 8 rad Integrating on both sides So wdw f20d0 0 dw do Xx do dt

Block A is placed on a rough wedge B which is placed on a smooth surface The wedge has angle of inclination of 53 and is imparted a horizontal acceleration g towards right Block A is given an initial velocity vo with respect to wedge Find the coefficient of friction for which block A moves with constant velocity vo with respect to wedge g 10 m s a 2 7 c 4 7 a g 114 B 53 Smooth surface b 3 7 d 1 3

a ert y 189 In the figure shown the horizontal surface is smooth and the strings are inextensible and massless pulleys are light If the acceleration of block 1 kg is a then acceleration of 3 kg is 1 Zero 3 kg 2 2a 3 4 8 2 E AT 1 kg 193 194

Find the acceleration of the hemisphere immediately after the system is released from rest There is no friction anywhere A B Rigid rod C M Auch fazar 37 Ac Ty Gna Ay G H adu a M mg M msin 0 R mg Mtan 0 m R Fixed vertical gap mg Mtane mcote Correct Answer ReR Greater R

23 Blocks A and B of masses 3m and 2m are connected by a spring and moving on a smooth horizontal plane xy plane as shown in the figure If instantaneous acceleration of A is a 21 31 m s what is the instantaneous acceleration of B y4 B ww O 1 2 51 3 m s 3 31 4 5 m s a www A X 2 61 1 5 m s2 4 3 5 i j m s 4 2

3 USE CODE BAHUBALI FOR 10 OFF ON PLUS ICONIC SUBSCRIPTION From v t graph shown in figure We can draw the following conclusions 1 between t Is to t 2s speed of particle is decreasing 2 between t 2s to t 3s speed of particle is increasing 3 between t 5 s to t 6 s acceleration of particle is negative 4 between t 0 to t 4s particle changes its directions of motion twice 1 A B 2 B C 3 C D 4 None

9 A block of mass m slides down an inclined plane which makes an angle with the horizontal The coefficient of friction between the block and the plane is u The force exerted by the block on the plane is A mg cos0 mg cos 0 C D mgcose 2 B 1 mg cos 0 2 1

2 A block B with a mass of 2 4 kg on an inclined plane with an angle of 40 is connected to another block A with a mass of 3 2 kg that is hanging over the top edge of the incline as shown in the diagram below B A The block A is moving downwards while the block B slides up the plane The coefficient of kinetic friction between the plane and the block B is 0 10 Calculate the magnitude of acceleration of the blocks and the magnitude of tension force in the string C 4

A block of mass M rests on smooth fixed inclined surface whose angle of inclination is as shown A horizontal force F is applied on the block The normal force applied by the block on the inclined plane is B 1 Mg sin F cos 3 Mg cos F sin 2 Mg sin F cos 4 Mg transistor

On an inclined plane of 30 a block mass m 4 kg is joined by a light cord to a uniform solid cylinder mass m 8 kg radius r 5 cm The coefficient of friction between the block and the inclined plane 0 2 Friction at the bearing is negligible There is no slipping between cylinder and incline plane Choose the correct option s m m A Acceleration of block is 4 25m s B Friction acting between cylinder and incline plane is 13 01N C Tension in the cord is 0 8 N

A string is connected to block of mass m 1 2 kg placed over rough table surface as shown in figure Calculate minimum vertical force F in Newton required to move the block Pulley and string are ideal and coefficient of friction between block and table surface is u 12 Take g 10 m s 37 37 F

45 A body hangs from a spring balance supported from the roof of an elevator If the elevator has an upward acceleration of 2 45 m s and the balance reads 50 newtons What is the true weight of the body Given g 9 8 m s A 50 N B 30 N C 40 N D 60 N

28 In the following figure triangular wedge is fixed All surfaces are smooth Pulley and string are id Find tension in the string 8kg 30 1 4 g 4kg 2 2g 3 g 15 AL 4 3g 2

11 A light inextensible cord supporting two identical loads at its ends passes over two ideal small pulleys fixed to a horizontal ceiling If the midpoint of the cord between the pulleys is gradually pulled downwards the pulling force F varies with displacement x of the midpoint according to the following graph Acceleration of free fall is 10 m s The distance between the pulleys is closest to a 5 m FIN 10 5 10 15 20 25 b 10 m 30x m

1 A constant retarding force 100 N is applied to a body of mass 20 kg moving initially with speed 20 m s How long does the body take to stop NCERT I XI Pg 110 1 2 s 2 3 s 3 1 s 4 4 s

to the ends of a massless string passing over a pulley of negligible weight The pulley itself is attached to a light spring balance as shown in figure The masses start moving during this interval the reading of spring balance will be 1kg 1 more than 6 kg 2 less than 6 kg 3 equal to 6 kg 4 none of the above FORSSAVIN 5kg

If acceleration of block m is a downward then acceleration of block m will be ca 30 1 2a upward 2 a upward 0 M a 3 upward 2 4 2a downward M

05 Inclined plane is moved towards right with an acceleration of 5ms 2 as shown in figure Find force in newton which block of mass 5 kg exerts on the incline plane All surfaces are smooth A 50 N C 55 N 5kg 5 m s 37 7 B 60 N D 70 N

1 An ideal system of pulley string spring is at rest as shown in the figure Acceleration of 5 kg block at the instant when the thread QR is burnt Spring constant k 200 N m OS bolev r 1 5 m s sah 0 5 kg 2 kg mim MUS A shoq q qart Pam Of 1 2 3 m s m 4 Zom adus

estion 1 The spring has a length of 1 5 m and the 10 kg block is at rest on the incline when a force of F 100 N applied to the block parallel to the plane Determine the velocity of the block after it moves 1 m dow the plane The unstretched length of the spring is 1 0 m The coefficient of friction between the plan and the block is pk 0 20 and the spring has a stiffness k 80 N m F 100 N 30

Six similar Bulbs are connected as shown in the 24 Six simil figure with a DC source of emf E and zero internal resistance The ratio of power consumption by the bulbs when i all are glowing and ii in the situation when two from section A and one from section B are glowing will be 1 4 9 A vo 00 E B 00 00 2 9 4 28 A cylindr constant magneti of the c figure B 1 2

Find the condition for system shown in the figure to be in equilibrium Assume all pulleys to be smooth and strings to be mass less M is mass of pulley A and M is mass of pulley B a mg 2F c M 2MB A 0 b Pulley A cannot be mass less d Pulley B cannot be mass less

A OT 60 kg is standing on a plank and holding a string passing over a system of ideal pulleys A mass of 10 kg hanging over a light pulley such that the system is in equilibrium The force exerted by the plank on the man is g acceleration due to gravity benidoo MS 08 S MOSA AT 1 20 g pa ni si swop 60 kg od prada lo 10 kg M 8 85 0 2 40 C T CA

Calculate the value of the acceleration of the following body if the force P 1100N and the coefficient of friction between the ground and the body is 0 P 30 O a 1 8 m s a 3 8 m s a 5 2 m s O a 12 8 m s 80 kg

A ball of mass 7 00 kg is hung by two cables attached to the walls as shown in the followin figure Calculate the tension in the horizontal cable 35 m 2 a 48 0 N b 83 5 N c 68 6 N d 93 5 N

Your brother calls you sounding desperate because his truck got stuck in a muddy patch near the top of a hill on his farm as he was hauling watermelons to the store When you arrive you realize you probably can t pull his heavy truck up the hill with your lightweight car But he has two pulleys and some rope and having just taken Physics 129 at Sunshine College you realize you might be able to pull him out if you could be driving down the other side of the hill The truck is a distance d 35 m from the top of the hill a First you do a quick calculation You know your car will accelerate from zero to 30 m s about 60 mph in 10 s on a horizontal road and you know the mass of your car is mc 1100 kg Using that information you calculate the force your car exerts against the road Find what it is 9 5

A uniform rope of length lies on a table If the coefficient of friction is u then the maximum length of th part of this rope which can overhang from the edge of the table without sliding down is 1 2 3 TIN

A string tied on a roof bears a maximum tension of 50 kg wt The minimum acceleration that can be acquired by a man of 98 kg to descend will be Take g 9 8 m s 1 9 8 m s 2 4 9 m s 3 4 8 m s2

A 2 0 kg block slides on a rough horizontal surface A force P 6 0 N is applied to the block as shown The magnitude of the block s acceleration is 1 2 m s2 What is the magnitude of the force of friction acting on the block 1 2 0 N 2 1 4 N 3 1 6 N 4 2 8 N ALT 30 2 0kg

The rock of mass m 2 30 kg is sitting on the vertical spring Calculate the value of t compressed length of the vertical spring with spring constant of 1 46 kN m A 15 4 cm B 1 54 cm C 0 54 cm D 1 43 cm

For given figure m is 30 kg mB mc 5 kg All contact surfaces are smooth g 10 m s Select the correct statements fyn ffm 30 kg mB mc 5 kg 1 A4 A ch uaz fah 31 g 10 m s T B A Acceleration of block A B and C are 1 m s 3 m s and 5 m s respectively A B C 1 m s 3 m s J 5 m s C A D B 350 N Bu qey Auch da 350 N Correct Answer Contact force between B and ground is Tension in string is 30 N 30 N Correct Answer Contact force between B and C is 15 N Beq quch da 15 N

1 There is a system which has two blocks Block B is on inclined plane and its kinetic coefficient of friction is 0 25 If this system is released block A will go downward and block B moves upward along the inclined plane Determine the acceleration of each block A m 50 kg B m 8 kg 58 44x 0 25 m

The upper half of an inclined plane with inclination is perfectly smooth while the lower half is rough body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for lower half is given by 1 2 sin A 2 2 cos 3 2 tan 4 tan USE BAHUBALI OR 10 OFF

55 Two trains are moving with velocities 10 ms and v 20 ms on the same track in opposite directions After the application of brakes if their retarding rates are a 2 ms and 1 ms respectively then the minimum distance of separation between the trains to avoid A collision is a 150 m b 225 m c 450 m d 300 m

2 A big boat is being pulled by two small boats as shown in Figure 2 If a resultant force R of 1000 N is needed to move the big boat find out the forces that act along the two ropes forces P and Q Given that 0 30 and 0 45 Plot the variation of the magnitude of the force Q if 0 varies from 10 to 80 Consider a step size of 10 25 Marks 2 KOHOD Figure 2 0 30 40 R

2 25 Three blocks A B and C of mass m each are arranged in pulley mass system as shown Coefficient of friction between block A and horizontal surface is equal to 0 5 and a force P acts on A in the direction shown The value of P mg so that block C doesn t move is

A small block of mass figure Height of vertical side of wedge is 5 m Now rest on the top of an inclined wedge as shown in wedge is pulled with a force of 10 3 N horizontally The normal reaction on the block is Take g 10 m s 1 Zero 3 15 N 30 1 kg 71 5 m as M 1 kg Disy lev elorio Isoil event stak 2 2N 4 2 N F

4 5 m s Figure shows a uniform rod of mass 3 kg and of length 30 cm The strings shown in figure are pulled by constant forces of 20 N and 32 N The acceleration of the rod is 10 cm 20 cm 1 2 m s2 2 3m s2 3 4 m s 4 6 m s2 20 N A B NIS LAI

A 60 kg body is pushed with just enough force to start it moving across a floor and the same force continues to act afterward The coefficients of static and sliding friction are 0 5 and 0 4 respectively The acceleration of the body is 2 A 6 ms 2 B 1 ms 2 C 2 5 ms D 3 8 ms 2

00358 Each of the three plates has a mass of 10 kg If the coefficients of static and kinetic friction at each surface of contact are 0 3 and 0 2 respectively g 10 ms 2 u The acceleration of block B is 1 zero 18N4 15N 2 3 336 m s D 103 C A 100N 3 4 11 m s 4 5 m s

Figure shows a block placed on a bracket Bracket is placed on a smooth floor it is pulled by 0 a force F 6N horizontally Block is projected with velocity v relative to bracket as shown in figure Find time in second after which it stops relative to bracket Horizontal surface of racket is smooth while vertical surface is rough Given m 1kg M 5kg v 4m s u 0 5 the motion of bracket is restricted in z direction 1 Rough Smooth

A 3 00 kg block is sent up a ramp inclined at an angle 0 29 0 from the horizontal It is given an initial velocity v0 15 0 m s up the ramp Between the block and the ramp the coefficient of kinetic friction is uk 0 50 and the coefficient of static friction is us 0 80 What distance D in m along the ramp s surface does the block travel before it comes to a stop

8 R 150 N is the resultant of four concurrent forces of which only three are known Find the fourth force in magnitude and direction 100N 120N Ans P 176 58 N 0 51 30 60 60 25 45 250N R 150N

1 a b 3 b d KNOOS 85 A car starts from rest and accelerates uniform by for 4 seconds and then moves with unifor velocity which of the x t graph represent the moti of the car 1 3 2 a c 4 c d L 2 4

D A hammer weighing 1 kg moving with the speed of 20 m s strikes the head of a nail driving it 20 cm into a wall Neglecting the mass of the nail calculate i the acceleration during the impact Ans 2000 m s ii the time interval during the impact and iii the impulso Ans 0 01s

A block rests on an inclined plane making an angle of 30 with the horizontal The coefficient of static friction between block and the plane is 0 8 If the frictional force on the block is 10 N then Mass of block in kg Take g 10 m s

Three equal weights of mass m each are hanging on a string passing over a fixed pulley as shown in Fig What are the tensions in the string connecting weights A to B and B to C A 7 4 mg 3 4 mg B 7 3 mg 4 3 mg C 4 3 mg 2 3 mg D 3 4 mg mg 4 a T MA B Cm

12 Two springs have their force constants in the ratio of 3 4 Both the springs are stretched by applying e force F If elongation in first spring is x then elongation in second spring is 1 3x 2 4x 3 4

Three blocks each of mass vertically with the help of inextensible strings and in ideal spring Initially the system was equilibrium At any instant lower most string is cut then acceleration of block B just after cutting the string is C 1 g JA OB c 2 ON 9

4 Problem 14 You are holding a cup of coffee Consider the following forces 1 The weight of the cup of coffee 2 the force that your hand exerts on the coffee cup and 3 the force the coffee cup exerts on your hand 50 Part a Which two of these forces have equal magnitude but opposite direction because of Newton s Third Law 2 and 3 Correct 50 Part b Which two of these forces have equal magnitude but opposite direction because of Newton s Second or First Law Grade 0 Correct Answer Student Final Submission Feedback