Newton's law of motion Questions and Answers

Two long current carrying thin wires both with current I are held by insulating threads of length L and are in equilibrium as shown in the figure with threads making an angle 0 with the vertical If wires have mass per unit length then the value of I is g gravitational acceleration a 2 ngL PO c sin 0 Owl tan 0 n gL Vui Po cos 0 Tom b L n gL V Mo d 2 sin 0 tan 0 n gL Ho cos 0 11

with angle of inclination 8 Various values of 0 are given in Column I The coefficient of friction between the 1 kg another mass m 2 kg are placed together see figure on an inclined plane block m and the plane is always zero The coefficient of static and dynamic friction between the block m and the plane are equal to 0 3 In Column Il expressions for the friction on block m are given Match the correct expression of the friction in Column II with the angles given in Column I and choose the correct option The acceleration due to gravity is denoted by g Useful information tan 5 5 0 1 tan 11 5 0 2 tan 16 5 0 3 A 5 B 0 10 C 8 15 D 8 20 Code A 1 P Mi Column I B P C p D r m m Column II p m g sine q m m g sine r m g cose s m m g cose

20 N 1 0 kg Figure 5 ES 5 Consider the situation shown in figure 5 E9 All the surfaces are frictionless and the string and the pulley are light Find the magnitude of the acceleration of the two blocks 0 98 N 1 F 3m 5m Figure 5 E9 m 4 m A constant force F m g 2 is applied on the block of mass m as shown in figure 5 E10 The string and the pulley are light and the surface of the table is smooth Find the acceleration of m Figure 5 E10 M F 1 0 kg 32 N Figure 5 E11 m 27 In figure 5 E11 m 5 kg m 2 kg and F 1 N Find the acceleration of either block Describe the motion of m if the string breaks but F continues to act Mag mitm 4 3 28 Let m 1 kg m 2 kg and m 3 kg in figure 5 E12 Find the accelerations of m m and m The string from the upper pulley to m is 20 cm when the system is released from rest How long will it take before m strikes the pulley 20cm m 29 In the previous problem suppose m 20 kg and m 30 kg What should be the mass m so that it remains at rest 2 M Figure 5 E12 30 Calculate the tension in the string shown in figure 5 E13 The pulley and the string are light and all surfaces are frictionless Take g 10 m s M 1 kg Figure 5 E13 31 Consider the situation shown in figure 5 E14 Both the pulleys and the string are light and all the surfaces are frictionless a Find the acceleration of the mass M b Find the tension in the string c Calculate the force exerted by the clamp on the pulley A in the figure B O Figure 5 E14 30 1 kg Figure 5 E15 MO 32 Find the acceleration of the block of mass M in the situation shown in figure 5 E15 All the surfaces are frictionless and the pulleys and the string are light 9 3 5N 2 M 29 13 Mg 13 2 Mg 3

8 A body is dropped from a certain height h h is very large and second body is thrown downward with velocity of 5 m s simultaneously What will be difference in heights of the two bodies after 3 s 2 10 m 4 20 m 3 15 m

Two blocks A and B of same mass m attached with a light spring are suspended by a string as shown in figure Find the acceleration of block A and Bjust after the string is cut A g 0 C g g B B 2g g g 2 D g mg kx Fos B A C

A particle moving with uniform retardation covers distances 18m 14m and 10m in successive seconds It comes to rest after travelling a further distance of 1 50 m 2x8m 3 12m 4 42m

discs of mass in and 4m having radii of a and 2a respectively are rigidly fixed by a massless rigid rod of length 1 24a through their centres This assembly is laid on a firm and flat surface and set rolling without slipping on the surface so that the angular speed about the axis of the rod is wo The angular momentum of the entire assembly about the point O is I see the figure Which of the following statement s is are true JEE Adv 2016 4m O a b m 2a 0 The centre of mass of the assembly rotates about the z axis with an angular speed of co 5 The magnitude of angular momentum of center of mass of the assembly about the point O is 81 ma co c The magnitude of angular momentum of the assembly about its center of mass is 17 ma 2

by a 10 Figure 6 W15 shows triang string placed on the two inclined parts of a structure The coefficients of static and kinetic fri are 0 28 and 0 25 respectively at each of the surface Find the minimum and maximum values of m for the system remains at rest b Find the acceleratio either block if m is given the minimum value calcul in the first part and is gently pushed up the inclin a short while m 45 45 Figure 6 W15 2 kg

23 arrangement shown below A m UL b g g 2m B Accelerations of masses A and B just after cutting the string Care a 0 g Dolc c sa d 2g g

15 The block of mass m shown in figure 12 E2 is fastened to the spring and the block of mass m is placed against it a Find the compression of the spring in the equilibrium position b The blocks are pushed a further distance 2 k m m g sine against the spring and released Find the position where the two blocks separate c What is the common speed of blocks at the time of separation from k mmmm my m 0 Figure 12 E2 19 kn m m 9 kn m gsin

A block of mass M and cylindrical tank which contains water having small hole at bottom Which is closed initially total mass of cylinder water is also M are attached at two ends of an ideal string which passes over an ideal pulley as shown At t 0 hole is opened such that water starts coming out of the hole with a constant rate kg s and constant velocity V relative to the cylinder Given that string Acceleration of the block at any time t will be always remains taut V gt A 2M ut ugt 2M t C B D V 2M ut 2 V 2M ut M

and the acceleration of the 500 g block in figure 5 E18 100 g 50 g 30 0 Figure 5 E18 500 g

Let m 1 kg m 2 kg and m 3 kg in figure 5 E12 Find the accelerations of m m and m The string from the upper pulley to m is 20 cm when the system is released from rest How long will it take before m strikes the pulley

5 In the above problem If the force F would have been applied on the bar of mass m then what would have been the maximum force F for no slipping of m of M The horizontal surface on which the plank is kept is smooth l E M

3 When a rubber band is stretched by a distance x it exerts a restoring force of magnitude F ax bx where a and b are constants The work done in stretching the unstretched rubber band by Lis D aL2 bL3 IIT Mains 2014 A aL bL aL bL 2 3 C A wire which passes through the hole in a small h B 1aL bL3 2 3

Example 5 6 Two cylinders P and Q rest in a channel as shown in Fig 5 13 B 60 Q P 180 mm D Fig 5 13 The cylinder P has diameter of 100 mm and weighs 200 N whereas the cylinder Q has diameter of 180 mm and weighs 500 N This point will be discussed in more details in the chapter of Principles of Friction

6 12 Figure shows a 5 kg ladder hanging from a string that is connected with a ceiling and is having a spring balance connected in between A boy of mass 25 kg is climbing up the ladder at acceleration 1 m s Assuming the spring balance and the string to be massless and the spring to show a constant reading the reading of the spring balance is Take g 10 m s 1 30 kg 2 32 5 kg 3 35 kg 4 37 5 kg

6 6 A bob is hanging over a pulley inside a car through a string The second end of the string is in the hand of a person standing in the car The car is moving with constant acceleration a directed horizontally as shown in figure Other end of the string is pulled with constant acceleration a relative to car vertically The tension in the string is equal to 1 mg cos 0 sin 8 ma 3 m g a ma m car a 2 2 m g a ma 4 m g a lock of mass M as shown

In the arrangement shown in Fig 1 24 the masses m of the bar and M of the wedge as well as the wedge angle a are known trolls The masses of the pulley and the thread are negligible The friction is absent Find the acceleration of the wedge M m Sa M Fig 1 24

Find the mass Mf of the hanging block in figure 5 E16 which will prevent the smaller block from slipping over the triangular block All the surfaces are frictionless and the strings and the pulleys are light 8 34 Find the acceleration of the blocks A and B in the three situations shown in figure 5 E17 A 4 kg 5 kg A B A 4 M 2 ko Figure 5 E16 A 29 Figure 5 E17 13 Joga 305 kg 1 b 3 100 g 50 g 30 Figure 5 E18 1 kg 500 g 291 3 35 Find the acceleration of the 500 g block in figure 5 E18 P A 09 c 2 kg K 36 A monkey of mass 15 kg is climbing on a rope with one end fixed to the ceiling If it wishes to go up with an acceleration of 1 m s how much force should it apply to the rope If the rope is 5 m long and the monkey starts from rest how much time will it take to reach the ceiling 165 TOS A monkey is climbing on a rope that goes over a smooth light pulley and supports a block of equal mass at the other end figure 5 E19 Show that whatever force the monkey exerts on the rope the monkey and the block Slo move initially both were change as time passes Figure 5 E19 The monkey B shown in figure 5 E20 is holding the tail of the monkey A which is climbing up The masses of the monkeys A and B are 5 kg a respectively If A can tolerate a tension of 30 tail what force should it apply on the rope in carry the monkey B with it Take g 10 m s 70N 100N Figure 5 E20 1 c 7 d 13 a 2 8 14 1 b d 4 a c 7 c d 1 10 N 39 Figure 5 E21 shows a man of mass 60 kg stand 2 3 1 10 a light weighing machine kept in a box of mass The box is hanging from a pulley fixed to the a 3 1 1 10 through a light rope the other end of which is h 4 5 N and the man himself If the man manages to keep th at rest what is the weight shown by the machine force should he exert on the rope to get his correct 6 0 25 Na 5 F 2 on the machine the mo m 7 F 1 777

Two blocks of mass M 20kg and M 12kg ar connected by a metal rod of mass 8 kg The system is pulled vertically up by applying a force of 480 N as shown in figure The tension at the mid point of the rod is IFF 1 0010 480 N M Mo

from rest when spring was in its natural length The pulley also has mass m but it is frictionless Suppose the value of m is such that finally it is just able to lift block M up after releasing it Column I i ii Tension in the rod when m is in equilibrium iii Weight of m required to just lift M iv Normal force acting on M when m is in equilibrium Tension in the string when displacement of m is maximum possible a b C d M Column II M 3 8 2 Mg 00 8 Knu 2 2 mg oooooo Ro Str

set into oscill What is the trajectory of the bob of its extreme positions b at its mean positio 3 A man of mass 70 kg stands on a weighing scale in a lift which is moving a upwards with a uniform speed of 10 m s b downwards with a uniform acceleration of 5 m s2 c upwards with a uniform acceleration of 5 m s What would be the readings on the scale in each case d What would be the reading if the lift mechanism failed and it hurtled down freely under gravity article of mass 4 kg What is

The coefficient of static friction between your hand and a pie plate is about 0 8 If you want to put a cream pie in someone s face what minimum acceleration do you need to keep it from sliding down your vertica hand A 4g 5 2g B 5 C 5 g 2 D 5g 4

In the figure the vertical sections of the string are long A is released from rest from the position shown Then DCE 2006 m vol 1 2 m A m a The system will remain in equilibrium b The central block will move down continuously c The central block will undergo simple harmonic motion d The central block will undergo periodic motion but not

the Example 6 5 A block of mass m is placed on the inclined surface of a wedge as shown in Fig 6 249 Calculate t acceleration of the wedge and the block when the block is released Assume all surfaces are frictionless m 340 0

Three particles start from origin at the same time with a velocity 2ms 1 along positive x axis the second with a velocity 6ms 1 along negative y axis Find the velocity of the third particle along x y line so that the three particles may always lie in a straight line a 3 3 b 3 2 d 2 2 c 3 2

5 Two blocks of mass 2kg are connected by massless ideal spring constant k 10N m The upper block is suspended from roof by a light inextensible strings A The spring is initially un stretched The lower block given an initial velocity downwards The minimum tension developed in the string connected to the ceiling is 2m s nearest to 1 10 N A 2kg fee e 2kg 2 20 N

29 Find the acceleration of the cylinder of mass m and radius R and that of plank of mass M placed on smooth surface if pulled with a force F as shown in figure Given that sufficient friction is present between cylinder and the plank surface to prevent sliding of cylinder 100 odt 1941 m odtru anillo bod M F P

A man of mass 50 kg carries a bag of weight 40 N on his shoulder The force with which the floor pushes up his feet will be 1 882 N 3 90 N 2 530 N 4 600 N

A sphere of mass m is kept between two inclined walls as shown in the figure If the coefficient of friction between each wall and the sphere is zero then the ratio of normal reaction N N offered by the walls 1 and 2 on the sphere will be A tane B tan20 0 A 1 C 2cos0 D cos20

The two pulley arrangements shown in the figure are identical The mass of the rope is negligible In a the mass m is lifted up by attaching a mass 2m to the other end of the rope In b m is lifted up by pulling the other end of the rope with a constant downward force of 2mg The ratio of accelerations in two cases will be a 1 3 b 1 2 c 1 1 d 1 4 a m 2m b m 2mg

30 Two objects of masses m and 2m are connected by a massless string passing over a fixed smooth pulley The acceleration of heavier mass w r t the lighter mass is 3 8g 3 2 2m 4g 3

4 on The ratio of acceleration of pulley to the acceleration of the block is string is inextensible m F A 0 5 B 2 C 1 Find the velocity of the hanging block if the velocities of the fron figure D None of these

23 What will be the value of maximum accelera of the truck in the forward direction so that the t kept on the back does not topple 1 ag h 2 hg a 3 ag 2h 4 h bg b h a

A constant force F 20 N acts on a block of mass 2 kg which is connected to two blocks of mas m 1 0 kg and m 2 kg as shown in Fig 3 HT 3 Calculate the accelerations produced in all s three blocks Assume pulleys are frictionless and weightless FIGURE 3 HT 3 F 20N M 2 kg T T o m T m a F4 R FIGURE 3 HT 4 Mg T 2T ta m18 T 192 m2g

The velocities of A and B are marked in the figure Find the velocity of block C assume that the pulleys are ideal and string inextensible Tim s A O B

Find acceleration of block in given figure 1 6 m s 3 1 m s 10kg 3750 N 37 2 11 m s 4 10 m s

down a frictionless hemispherical bowl It passes the point A at t 0 At this instant of time C the horizontal components of its velocity are v A bea Q of the same mass as P is ejected from A att 0 alon the horizontal string AB with the speed v Frictio between the bead and the string may be neglected Le tp and to be the respective time taken by P and Q reach the point B Then fe tp ta c tp tq b tp tQ d p length of arc ACB D

A sphere of mass m is held between two smooth inclined walls For sin 37 3 The normal reaction of the wall 2 is equal to 2 A 37 37 mg Correct Answer mg sin 74 mg cos 74 None of theso SWING

the driver thrown e in touch we would f the bus and the owever een the sudden ictional ur feet strictly s some parts go with ere it is ore we opens of the e body opens p due lative e bus move ward e into ally hip ta the ter hat Exert hall nal the grens is Momentum Momentum of a body is defined to be the product of its mass m and velocity v and is denoted by p 5 1 Momentum is clearly a vector quantity The following common experiences indicate the importance of this quantity for considering the effect of force on motion p mv Suppose a light weight vehicle say a small car and a heavy weight vehicle say a loaded truck are parked on a horizontal road We all know that a much greater force is needed to push the truck than the car to bring them to the same speed in same time Similarly a greater opposing force is needed to stop a heavy body than a light body in the same time if they are moving with the same speed If two stones one light and the other heavy are dropped from the top of a building a person on the ground will find it easier to catch the light stone than the heavy stone The mass of a body is thus an important parameter that determines the effect of force on its motion the mos Same Sper Speed is another important parameter tout heavy consider A bullet fired by a gun can easily pierce human tissue before it stops resulting in casualty The same bullet fired with moderate speed will not cause much damage Thus for a given mass the greater the speed the greater is the opposing force needed to stop the body in a certain time Taken together the product of mass and velocity that is momentum is evidently a relevant variable of motion The greater the change in the momentum in a given time the greater is the force that needs to be applied A seasoned cricketer catches a cricket ball coming in with great speed far more easily than a novice who can hurt his hands in the Ono raggon in that the cricketer allows a both Stone tene sequire force to stopte a light stone

Which one of the following statements is not true about Newton s second law of motion F m a The second law of motion is consistent with the first law b The second law of motion is a vector law c The second law of motion is applicable to a single point particle d The second law of motion is not a local law

M M 18 Calculate the tensions T T and T3 in the three threads shown in the following figure All threads are massless g 10 m s T 137 T 5 T 4 kg 1 30 N 40 N 50 N 2 50 N 30 N 40 N 3 35 N 45 N 40 N 4 30 N 50 N 40 N 19 A heavy block of mass M hangs in equilibrium at the end of a rope of mass m and length connected to a

2 A car moving at 40 km h is to be stopped by applying brakes in the next 4 0 m If the car weighs 2000 kg what average force must be applied on it

A block of mass 10 kg is placed on a long trolley The coefficient of friction between the block and trolley is 0 2 The trolley accelerates from rest with 0 5 m s for 20 s then what is the friction force 1 20 N 2 100 N 3 5 N 4 10 N

m m The magnitude of normal reaction between the blocks is

om rest and undergoes an acceleration 131 A particle as shown in figure The velocity time graph from figure will have a shape a c VA a m s a a 1 2 3 4 A b d t

4 Initially spring is in its natural length Now a block of mass 0 25 kg is kept as shown Find out maximum force by system on floor when block of mass 0 25 kg oscillates with amplitude psMmo01 1 2 cm and angular frequency 20 rad s 1 22 50 N m m 0 25kg 000000000000 M 2 kg 2 23 75 N

The blocks A B are of masses 3 kg and 5 kg respectively The inclined plane is smooth Assume g 10 m s The contact force between the blocks A B in the cases a and b are take g 10 m s a AB 30

A rocket starts moving upwards with gases ejecting at a rate of 2000 m s relative to itself After 2 minutes its fuel burns out and its mass reduces to 1 5 of its initial value then its velocity at that instant will be 1 1021 m s mm 2 4048 m s