Newton's law of motion Questions and Answers

c 96 N 96 N d 36 N 36 N 4 Two blocks each of mass M are resting on a frictionless inclined plane as shown in Then 260 figure a The block A moves down the plane b The block B moves down the plane c Both the blocks remain at rest d Both the blocks move down the plane

d A body of mass 2 kg travels according to the law x t pt qt rt where p 3 ms q 4 m and r 5 ms The force acting on the body a t 2 seconds is a 136 N c 158 N b 134 N d 68 N

00 A mass of 1 kg is suspended by means of a thread The system is i lifted up with an acceleration of 4 9 ms ii lowered with an acceleration of 4 9 ms The ratio of tension in the first and second case is a 3 1 c 1 3 b 1 2 d 2 1

2 7 A block of mass M rests on a block of mass M which lies on a frictionless table The coefficient of friction between the blocks is What is the maximum horizontal force which can be applied to the blocks for them to accelerate without slipping on one another if the force is applied to a block 1 and b block 2

95 In the system shown in the figure the acceleration of 1 kg mass is a 4 downwards b c upwards d upwards downwards 4 kg 1 kg c I 5 d T g 98 A bo betwe reacti a 0 c 90 Two 00

c 81 A disc revolves with a speed 33 rev min and ha a radius of 15 cm Two coins A and B are placed a 4 cm and 14 cm away from the centre of the dise If the coefficient of friction between the coins and the disc is 0 15 which of the coins will revolve with the record a A c Both A and B b B d Neither A nor B

A spring balance is attached to the ceiling of a lift spring A man hangs his bag on the spring and the reads 49 N when the lift is stationary If the lif moves downward with an acceleration of 5 m s the reading of the spring balance will nearly be equal to 1 24 N 2 74 N 3 15 N 4 49 N A har

S 90 Block A of weight 100 N rests on a frictionless inclined plane of slope angle 30 as shown in the figure A flexible cord attached to A passes over a frictionless pulley and is connected to block B of weight W Find the weight W for which the 13 system is in equilibrium a 25 N b 50 N c 75 N d 100 N 81 Two blocks of masses 10 kg and 20 ke are connected

gravity 98 A book is lying on the table What is the ange between the action of the book on the table and the reaction of the table on the book b 45 a 0 c 90 d 180

A rod of mass m and length L is suspended from the ceiling with the help of two light inextensible cords each of length so that the rod is horizontal The rod is given an angular velocity about it central vertical axis Find increment in the tensile force in a cord immediately after the rod is given the angular velocity m 1 kg L 2 meter 1 1 meter 2 rad sec

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 AF EOK O O F 2m F 2m Fx 2m a F a a X X a 2 a x 2 x P

b 45 N d 65 N a 35 N c 55 N 87 A helicopter of mass 2000 kg rises with a vertical acceleration of 15 m s The total mass of the crew and passengers is 500 kg Choose the correct statements from the following Take g 10 ms i The force on the floor of the helicopter by the crew and passengers is 1 25 x10 N vertically downwards ii The action of the rotor of the helicopter on the surrounding air is 6 25 x10 vertically downwards iii The force on the helicopter due to the surrounding air is 6 25 x10 N vertically upwards b ii and iii d All the three a i and ii c i and ii J A 92 J 4 93

Laws of SOLVING PROBLEMS IN MECHANICS 85 An iron block of sides 50 cm x 8 cm x 15 cm has to be pushed along the floor The force required will be minimum when the surface in contact with ground is a 8 cm x 15 cm surface b 50 cm x 15 cm surface c 8 cm x 50 cm surface d force is same for all surfaces 16 Figure shows a man of 90

c 15 m s d 0 5 ms 2 The coefficient of static friction between the box and the train s floor is 0 2 The maximum acceleration of the train in which a box lying on its floor will remain stationary is Take g 10 ms a 2 ms 2 c 6 ms 2 b 4 ms2 d 8 ms of mass 1 kg lies on a horizontal surface in coef surfa with what fall c 69 In f frict the b

is and rce Da me ma to 48 There are four forces acting at a point P produced by strings as shown in figure which is at rest The forces F and F are IN

d 0 2 ms at an angle of tan w rt 8 N force 50 A body is moving under the action of two forces F 21 5j F 3 4j Its velocity will become uniform under a third force F given by a si j c Si j lock of mass b si j d 5i 9 d Flow 56 A girl pr vertical w frictional a down c out fr 57 A car acc force exer a the en

Which of the following observations would be adequately explained by Newton s third law 1 When turning a corner a passenger in a car feels pushed against the door 2 The friction of a surface causes a sliding object to come to rest 3 A car s tires slip on an ice covered surface 4 One skater pushes against another and both move off in opposite directions 5 The Earth is held in orbit around the Sun by a gravitational force of attraction

Laws of Motion 61 A block of mass 10 kg is placed on rough horizontal surface whose coefficient of friction is 0 5 If a horizontal force of 100 N is applied on it then 67 acceleration of the block will be g 10 ms Take a 10 ms c 15 ms2 b 5 ms2 d 0 5 ms ficient of statis friction between the box and a c In ti is a 68 The 40 coef mut

11 Two blocks A and B of masses 2m and 4m respectively are connected to each other by an ideal spring The whole system is suspended with the help of an inextensible string as shown in the figure If the system is initially in equilibrium then the acceleration of A just after cutting the string is 1 4 2 g B A 2 2g

TB 2 24 A device called a capstan is used aboard ships in order to control a rope which is under great tension The rope is wrapped around a fixed drum usually for several turns the drawing shows about three fourths turn The load on the rope pulls it with a force TA and the sailor holds it with a much smaller force TB Can you show that TB TA where is the coefficient of friction and is the total angle sub tended by the rope on the drum

d A B C D p 32 A rocket is going upwards with accelerated motion A man sitting in it feels his weight increased 5 times his own weight If the mass of the rocket including that of the man is 1 0 10 kg how much force being applied by rocket engine Take g 10 mij b 5 10 N a 5 10 N d 2 10 N c 5 10 N

1 37 A street car moves rectilinearly from station A to the next station B with an acceleration varying according to the lawf a bx where a and b are constants and x is the distance from station A The distance between the two stations the maximum velocity are A X C x 2a V b max a 26 V max a b b a das B x D x b 2a a b V max max 0 6 a b a b

38 A rocket with a lift off mass 2 x10 kg is blasted upwards with an initial acceleration of 5 ms The initial thrust of the blast is Take g 10 m s a 2 10 N b 3x10 N c 4 10 N d 5x10 N 39 A hall of mass m strikes a rigid wall 44

The massless pulley P is moving vertically downwards with constant speed of 15 m s Find the velocity in m s with which the block Q moves up at the instant shown All pulleys are fictionless Q 37 P 15m s 37 Space for Rough Work

Two blocks of masses 3m and 2m are in contact on a smooth table A force P is first applied horizontally on block of mass 3m and then on mass 2m The contact forces between the two blocks in the two cases are in the ratio A 1 2 C 3 2 P 3m 2m P B 2 3 D 5 3

1500 N DOM B 2000 N Q3 As shown in figure find that at what distance body A will attain a velocity of 3 m s when starts from rest Assume the coefficient of Friction as 0 2 and pulleys are frictionless and weightless

A ball is dropped from a height h above a massive platform that is moving upward with a constant speed u If the ball collides with the platform elastically find height above its initial position the ball will rebound Acceleration of free fall is g 2u Juzezgh

9 A body of mass 0 4 kg starting at origin at t 0 with a speed of 10 m s in the positive x axis direction is subjected to a constant F 8 N towards negative x axis The position of the body after 25 s is a 6000 m b 8000 m c 4000 m d 7000 m

c 2 5 N d 5 N 15 A bullet of mass 40 g moving with a speed of 90 ms enters a heavy wooden block and is stopped after a distance of 60 cm The average resistive force exerted by the block on the bullet is a 180 N b 220 N c 270 N d 320 N 16 A body under the action of a force E bi

acceleration of the spool axis 256 A uniform solid cylinder of mass m rests on two horizontal planks A thread is wound on the cylinder The hanging end of the thread is pulled vertically down with a constant force F Fig 1 62 W F Fig 1 61 Fig 1 62 Find the maximum magnitude of the force F which still does not bring about any sliding of the cylinder if the coefficient of friction between the cylinder and the planks is equal to k What is the acceleration w of the axis of the cylinder rolling down the inclined plane 257 A spool with thread wound max

A material of the body C length of the rod D none of the above A horizontal tube open at both ends contains a column of liquid The length of the liquid column does not changes with temperature Let y co efficient of volume expansion of the liquid and a cofficient of linear expansion of material of the tube A y a B Y 2a C y 3a D y 0 in damped firmly at each end when its temperature is 25 C so that it imately 10 5 C y 2 1011

The 3 kg mass A has an acceleration of 3 2 m s in the upward directio Exam Do no 60 B Exam Do not questions A c 18 N d 19 5 N e None of the above What is the tension in the cable at B post questions a 15 N b 16 5 N

A block of mass 15 kg is placed over a frictionless horizontal surface Another block of mass 10 kg is placed over it that is connected with a light string passing over two pulleys fastened to the 15 kg block A force F 80 N is applied horizontally to the free end of the string Friction coefficient between two blocks is 0 6 The portion of the string between 10 kg block and the upper pulley is horizontal Pulley string connecting rods are massless Take g 10 m s The magnitude of acceleration of the 10 kg block is A 3 2 m s B 2 0 m s Smooth C 1 6 m s The magnitude of acceleration of the 15 kg block is A 4 2 m s B 3 2 m s C 16 3 m s 10 kg 0 6 15 kg D 0 8 m s D 2 0 m s F

B Collar A and block B are connected by a cable passing over three pulleys C D and E as shown Pulleys C and E are fixed while D is attached to a collar which is pulled downward with a constant velocity of 75 mm s At t 0 collar A starts moving downward from position K with a constant acceleration and no initial velocity Knowing that the velocity of collar A is 300 mm s as it passes through point L determine the change in elevation the velocity and the acceleration of block B when collar A passes through L

2 6 In the system of pulleys shown what should be the value of m such that 100 gm remains at rest Take g 10 m s A 180 gm B 160 gm C 100 gm D 200 gm P P2 100gm 4 m 200gm Figure 2 135 orizontal surface

2 30 A block of unknown mass is at rest on a rough horizontal surface A horizontal force F is applied to the block The graph in the figure 2 150 shows the acceleration of the block with respect to the applied force The mass of the block is Acceleration m s a 1 0 kg 2 0 kg 2 4 6 8 10 Applied force F N Figure 2 149 B 0 1 kg D 0 2 kg 12 14

slide between two perpendicular wall as shown in figure If the end A moves to the right with speed v then find the speed of the centre of the rod in terms of 1 v cote V 2 cote 2 3 V 2sine B xy 22 X A

A boy throws four stones of same shape size and weight with equal speed at different initial angles with the horizontal line If the angles are 15 30 45 and 60 at which angle the stone will cover the maximum horizontally 1 30 2 45 3 60 4 15

Two blocks are in contact on a frictionless table A horizontal force is applied to the larger block as shown in Fig 5 50 a If m1 2 3 kg m2 1 2 kg and F 3 2 N find the magnitude of the force between the two blocks b Show that if a force of the same magnitude F is applied to the smaller block but in the opposite direction the magnitude of the force between the blocks is 2 1 N which is not the same value calculated in a c Explain the difference any

3 A mass of 10 kg is suspended by a rope of length 4 m from the ceiling A force F is applied horizontally at the mid point of the rope such that the top half of the rope makes an angle of 45 with the vertical Then F equals Take g 10 ms 2 and the rope to be massless 1 100 N 2 90 N 4 70 N 3 75 N

99 A particle stays at rest as seen in a frame We can conclude that a the frame is inertial b resultant force on the particle is zero c the frame may be inertial but resultant force on the particle is zero d the frame may be non inertial but there is a non zero resultant force

A steel ball of mass 50 g is thrown vertically downwards with a velocity of 15 ms 1 from a height of 20 m it buries itself in the sandy ground to a depth of 20 cm the magnitude of average force exerted on the ball by the sand is nearly g 10ms 2 Assume resistance offered by sand is constant throughout

Joel is walking on a tightrope over Niagara falls When he is 250 m from one side of the falls and 350 m from the other side of the falls the tightrope is stretched downward a distance of 50 m If the force of gravity on Joel is 666 N find the tension in each side of the rope Hint Draw a diagram Use the distances to find the angles 6

A horizontal force F is applied to a frictionless pulley of mass m The horizontal surface is smooth Acceleration of the blo of mass m is e 2 3 F m 4m 2F m 4m F 4m M 2F 4m M m F

A weight hangs from a wire that is attached to two walls as shown on the right The system is in static equilibrium Which of the following correctly describes the relative tensions T and T on each side of the weight T1 T2 T1 T2 T1 T2 Not enough information is given T T

Choose the correct answer 1 A cubical block A of mass 10 kg and a block B mass 2 kg are connected via string pulley syster as shown in the figure If one end of the string i pulled with a force 20 N as shown then th acceleration of wedge will be All surfaces an smooth Pulley and strings are ideal F 20 N 16 1 4 m s 2 2 m s 3 1 m s 4 8 m s A B

Imagine that you are travelling in a space vehicle orbiting around the Earth You are provided with two identical boxes One is filled with sand and the other is filled with feathers How can you tell which is which without opening the boxes 1 By weighing using a common balance 2 By weighing using a spring balance 3 By simply holding the boxes in your hand 4 By giving a gentle horizontal push and

A cord passing over a frictionless massless pulley has a 4 0 kg object tied to one end and a 12 kg object tied to the other Compute the tension in the cord OA 9 8 N B 48 N

track in vertical plane which transforms into a circular arc of radius R Find the reaction force exerted at the bottom most position 3R 6mg 2 7mg 3 5mg 4 9mg m R ZEE N mu 0

In the arrangement show in Fig the masses of the wedge M and the body m are known The appreciable friction exists only between the wedge and the body m the friction coefficient being equal to k The masses of the pulley and the thread are negligible Find the acceleration of the body m relative to the ground M m