Newton's law of motion Questions and Answers

A rigid massless rod AB of length 1m is placed horizontally on two rigid supports at its ends as shown in figure A weight 10N is hung from a point C at a distance 30cm from A Find the reactions at the supports A and B respectively A 5 N 5 N B 3 N 7 N C 10N B

1 X X 2 x x 3 both x x and x X 4 Neither at x x nor X X 3 A chain of mass M 9 kg and length L 10m initially rests on a horizontal frictionless surface if it is slightly pushed down the horizontal surface due to which the chain starts sliding down then calculate closest value of the rate at which work is done on the chain by the gravitational force at the instant one third of the chain is hanging vertical Neglect all dissipative forces AD 1 173 W 3 300 W 2 150 W 4 100 W L 3 that it is in equilibrium In the figure

The axle of a pulley of mass m 1 kg is attached to the end of a spring of spring constant k 200 N m whose other end is fixed to the ceiling A rope of negligible mass is placed on the pulley such that its left end is fixed to the ground and its right end is hanging freely from the pulley which is at rest in equilibrium We begin to pull the endpoint A at the right end of the rope by a constant vertical force of F 15 N Friction can be neglected between the rope and the pulley Find the maximum displacement of point A after applying F Express your answer in cm Imma m D F

29 A block of mass m is attached to a spring and placed on an inclined plane The spring has a spring constant k and there is negligible friction between the block and inclined plane The block is released from rest at the position shown in the figure above with the spring initially unstretched What distance d does the block slide down the plane before coming momentarily to rest A B C D 2mg k mg k mg sin 0 k 0 2mg sin 0 k

such that the mass m remains stationary with respect to block of mass M as shown in the figure The magnitude of force P is A B C D P M m g tan P M m g P M m g sin P M m gCos P M m P m M B a 1 Vodent

Four persons are holding a rope of length at position as shown in figure All of them are applying equal force F in the direction as shown in figure Then the tension Statement 1 at point A will be F Statement 2 at point B will be 2F Statement 3 at point C will be F A only statement 1 2 is true C all the three statements are true FE 1 3 3 3 A F B B only statement 2 is true DI C

A particle moving in the positive x direction has initial velocity vo The particle undergoes retardation kv where v is instantaneous velocity The velocity of the particle as a function of time is 1 V 3 v Vo 1 kvot kt 2 v 4 v 2v 1 kt Vo 1 k v t

98 cms lems For Practice D ms 1 g bullet leaves a rifle with a velocity of s 1 and the rifle recoils with a velocity of ms Find the mass of the rifle Ans 15 kg kg shell is flying at a speed of 72 kmh It 1 HINTS 2 Proce 8 Let p be the Then

A block of mass M is pulled vertically upwards through a rope of mass m by applying force F on one end of the rope What force does the rope exert on the block F M m

A person 40 kg is managing to be at rest betwee vertical walls by pressing one wall A by his hands and feet and the other wall B by his back figure 6 E11 Assume that the friction coefficient between his body and the walls is 0 8 and that limiting friction acts at all the contacts a Show that the person pushes the two walls with equal force b Find the normal force exerted by either wall on the person Take g 10 m s B A

A gun weighing 10 kg fires a bullet of 30 g with a velocity of 330 ms With what velocity does the gun recoil What is the combined momentum of the gun and bullet before firing and after firing Ans 99 cms zero before and after firing 1

0 A particle of mass m is kept on a fixed smooth sphere of radius R at a position where the radius through the particle makes an angle of 30 with the vertical The particle is released from this position a What is the force exerted by the sphere on the particle just after the release b Find the distance travelled by the particle before it leaves contact with the sphere

A force acting on a particle of mass 200 g displaces it through 400 cm in 2 s If the initial velocity of t particle is zero then the magnitude of the force is a 0 4 N b 4 N c 40 N d 400 N ATINUM PACKAGE

6 8 3 M m m M m M 9 System shown in figure is in equilibrium and at rest The spring and string are massless Now the string is cut The acceleration of mass 2m and m just after the string is cut will be mg ma 3mg 2mg 2ma g 2 upwards g downwards 3 g upwards 2g downwards eeeeee 2 g upwards g 2 downwards 4 2g upwards g downwards

Using the law of conservation of momentum obtain the equation of motion of a rocket in free space A rocket starts from rest with an initial mass M and reaches a final velocity v when its mass is Mf show that e vret where Vret is the exhaust velocity A significant amount of energy in the Mo exhaust gases in any rocket flight is lost to heat and light Does this have any impact on the final

Illustration 7 11 A block of mass M is being pulled with the help of a string of mass m and length L The horizontal force applied by the man on the string is F M m Fig 7 51 Pull Determine a Find the force exerted by the string on the block and acceleration of system b Find the tension at the mid point of the string c Find the tension at a distance x from the end at which force is applied Assume that the block is kept on a friction less horizontal surface and the mass is uniformly distributed in the string

As shown in the following figure consider three arrangements A B and C where the pulleys are ideal strings are light and inextensible balls attached at the ends of the strings are identical and surfaces where the balls rest are frictionless Identify nature of equilibria i e stable unstable or neutral of the arrangements

Example 7 Figure a and b show the field lines of a positive and negative point charge respectively m c d a b a Give the signs of the potential difference Vp Vai VB VA b Give the sign of the potential energy difference if a small negative charge is moved from points Q to P from point A to B Give the sign of the work done by the field in moving a small positive charge from Q to P Give the sign of the work done by the external agency in moving a small negative charge from B to A e B 1 e Does the kinetic energy of a small negative charge increase or decrease in going from B to A a As Vx Thus Vp Vo Thus Vp Vo is positive Also V is less negative than VA VB VA or VB VA is positive b A small negative charge will be attracted towards positive charge The negative charge moves from higher potential energy to lower potential energy Therefore the sign of potential energy difference from Q to P is negative Similarly PE PE and hence sign of potential energy differences is negative c In moving a small positive charge from Q to P work has to be done by an external agen against the electric field Therefore work done by the field is negative d In moving a small negative charge from B to A work has to be done by the external agen It is positive Due to force of repulsion on the negative charge velocity decreases and hence the kin

5 A box is kept in the rear of a truck that is travelling on a level road The coefficient of sliding friction between box and truck bed is 1 3 The driver suddenly applies the brakes producing a deceleration g 2 Acceleration of box with respect to road is 1 g 2 forward 2 g 2 backward 3 g 3 forward

4 Two bodies of masses m and m moving on the same direction with velocities u U velocities after collision are V and V If each sphere loses the same amount of kinetic energy then and collide The 2 U U V V 0 4 U U V V 0 131 1 u U V V 0 3 u U V V 0 M ftor collision the ba

F F A whispering room is one with an elliptically arched ceiling If someone stands at one focus of the ellipse and whispers something to his friend the dispersed sound waves are reflected by the ceiling and concentrated at the other focus allowing people across the room to clearly hear what he said Suppose such gallery has a ceiling reaching 17 above the five foot high vertical walls at its tallest point so the cross section is half an ellipse topping two vertical lines at either end and suppose the foci of the ellipse are 21 feet apart What is the height of the ceiling above each whispering point height above whispering point feet above the floor

purp wearing out of the rail P 5 32 A block of mass 25 kg is raised by a 50 kg man in two different ways as shown in yields to a normal force of 700 N which mode should the man adopt to lift the block Fie 5 19 What is the action on the floor by the man in the two cases If the floor without the floor yielding 25 kg a 25 kg b

5 A child is sitting at one end of a long trolley moving with a uniform speed v on a smooth horizontal track If the child starts running towards the other end of the trolley with a speed u w r t trolley the speed of the centre of mass of the system will a u v c v b v u d none

A dumbbell is constructed by fixing small balls each of mass m at the ends of a light rod of length 1 The dumbbell stands vertically in the corner formed by a frictionless wall and frictionless floor After the bottom end is slightly pushed to the right the dumbbell begins to slide Denoting acceleration due to gravity by g if any time t the upper ball is leaving the wall then at that instant A Tension in the rod is zero B Acceleration of lower ball is zero 8g C speed of lower ball is m s V27 2

Consider the following spring mass system The masses m and m both are equal to 2 kg If mass m is suddenly removed when the system was in equilibrium and in rest then the amplitude of oscillation of the system will be spring constant k 100 N m ellele m m 0 4 m 0 1 m 0 8 m 0 2 m

The contact force exerted by a body A on another body B is equal to the normal force between the bodies We conclude that a the surfaces must be frictionless b the force of friction between the bodies is zero c the magnitude of normal force equals that of friction d the bodies may be rough but they don t slip on each other

38 In the figure shown the block B moves with velocity 10 ms The velocity of A in the position shown is a 12 5 ms b 25 ms B 37 c 8 ms 1 d 16 ms

Let F F and f denote the magnitudes of the contact force normal force and the friction exerted by one surface on the other kept in contact If none of these is zero a F F b F f c FN f d FN f F FN f N

30 30 a b The man pushes pulls with a force of 200 N The child and sled combo has a mass of 30 kg and the coefficient of kinetic friction is 0 15 For each case What is the frictional force opposing his efforts What is the secoloration of the child

Two cubes of masses m and m lie on two frictionless slopes of the block A which rests on horizontal table the cubes are connnected by a string which passes over a pulley as shown in fig To what horizontal acceleration f the whole system i e the block and cubes be subjected so that the cubes do not slide down the planes What is the tension in string

Block A and B of mass 2 kg and 4 kg are suspended through a string using a pulley inside an elevator moving downward with constant acceleration 2 m s The tension in the string which is joining two blocks 64 1 N A 2 B 32 3 N 2 m s 3 N 3 4 16 3 N 5

Two blocks of masses 5 kg and 10 kg are attached with the help of light string and placed on a rough incline as shown in the figure Coefficients of friction are as marked in the figure The system is released from rest Determine the acceleration of the two blocks 10kg P 0 3 37 50 Fixed 5kg H 0 1

rod is fixed between a vertical wall and a horizontal surface A smooth ring of mass 1 kg is released from rest which can move along the rod as shown At the release point spring is vertical and relaxed The natural length of the spring is 3 1 m Rod makes an angle of 30 with the horizontal Ring again comes to rest when spring makes an angle of 30 with the vertical rellele 30 A Force constant of the spring is 3 1 N m 2 B Maximum displacement of ring is 3 1 C Maximum extension in the spring is 3 m D Normal reaction on ring due to rod when it again comes to rest is 3 1 N m

7 Find F for system to be in equilibrium in newton 20 N 2 kg F A 370 B 3 kg Smooth

16 Two steel balls A and B are placed inside a right circular cylinder of diameter 54 cm making contact at points P Q and R as shown The radius TA TB 12 cm and B 18 cm The masses are ma 15 kg and 60 kg The forces exerted by the floor at the point Q and the wall at R are respectively taking g 10 m s P a 600 N 150 N N ONL A 154 cm B R b 750 N 150 N T

5 Find the resultant y Z force on block in newton 4 N X m 3 N smooth upot sorol

In figure tensions in string that connects masses A B is T that in string connecting B T and C is T then I s m m m3 m4 T quu a 2 A m Ma D b 0 5 c 4 Pupo mil B m C d 0 25

6 Make FBD Find net force g 10m s in terms of i and along ve y direction 30 N 490 N 5 kg X

The given figure shows two blocks each of mass m The system is released from rest If accelerations of blocks A and B at any instant not initially are a and a respectively then 1 a a cos 0 3 a a B To 2 a a cos 0 4 None of these A a

6 A rope of negligible mass passes over a pulley of negligible mass attached to the ceiling as shown in figure One end of the rope is held by student A of mass 70 kg who is at rest on the floor The opposite end of the rope is held by student B of mass 60 kg who is suspended at rest above the floor The minimum acceleration a with which the student B should climb up the rope to lift the student A upward off the floor A m s B m s Student A 70 kg Student B 60 kg C m s D 5 m s

2 In the setup shown a thread is taut between a nail A on a wall and a nail B on an inclined plane as shown in the figure You can change the length of the thread by changing location of the nail B A bead that can slide on the thread without friction is released from the nail A What should the length of the thread be so that the bead reaches the nail B in shortest time a h c h sec 0 50 b h cose d h cos 0 sec 0 50

B 2 In the setup shown a thread is taut between a nail A on a wall and a nail B on an inclined plane as shown in the figure You can change the length of the thread by changing location of the nail B A bead that can slide on the thread without friction is released from the nail A What should the length of the thread be so that the bead reaches the nail B in shortest time a h c h sec 0 50 b h cos 0 d h cos 0 sec 0 50

Calculate the tension T in the rope at a distance x from end A in the following diagram assuming F F F 63 rel B F B M x

Example 9 A sphere of radius 0 1m and mass 8 kg is attached to the lower end of a steel wire of length 5 0 m and diameter 10 3 m The wire is suspended from 5 22 m high ceiling of a room When the sphere is made to swing as a simple pendulum it just grazes the floor at its lowest point Calculate the velocity of the sphere at the lowest position Young s modulus of steel is 1 994 x 10 N m 11 OL wo have

A uniform rope of mass M and length L is placed on a smooth horizontal surface A horizontal force F is acting at one end of rope Calculate the tension in the rope at a distance x as shown 14 X M T F

Three massless pulley as shown in figure The acceleration of blocks will be g 10 m s m 4 kg m 2 kg m3 4 kg are connected with ideal strings passing over a smooth 3 N 1 2 m s 3 m s 4 m m T m 2 4 tension in the string connected between blocks is A 4 m s 5 m s

c 200 g 14 A light uniform spring is tied between the ceiling and the floor keeping the spring vertical as shown in the figure A bead of finite mass is glued at a distance 1 from the upper end of the spring and then allowed to move gradually downwards The bead shifts a distance y to come in equilibrium This experiment is repeated for different values of 1 Which 1 of the following graph shows the best dependence of y on

In give figure expansion of spring will be take g 10 m s 1 64 cm 3 32 cm 2kg u leeeeee a 2 m s k 100N m 4kg 2 16 cm 4 None

Ten identical cells connected in series are needed to heat a wire of length one meter and radius by 10 C in time t How many cells will be required to heat the wire of length two meter of the same radius by the same temperature in time t 1 10 2 20 3 30 4 40

A smooth block is released at rest on a 45 incline and then slides a distance d The time taken to slide is n times as much to slide on rough incline than on a smooth incline The coefficient of friction is 2005 1 k 1 3 s 1 2 HK 4 Hs 1 1 n