Newton's law of motion Questions and Answers

24 A body is projected up with a velocity 50ms after one second if accelaration due to gravity disappears then body 1 floats in air 2 continue to move up with constant velocity 3 continue to move up with acceleration 4 goes up and falls down 6 c r 1 a 3

39 An electron of mass m charge e falls through a distance h meter in a uniform electric field E Then time of fall t c t 2hm eE 2eE hm b t 2hm eE d t 2eE hm Karnataka C

A body A of mass 500 g is kept on a smooth table Fig 1 56 A is connected to one end of a string to the other end of which a body B of mass 200 g is attached The string passes over a frictionless pulley At time t 0 A is 200 cm away from the edge of the table and is moving with a velocity of 50 cm s 1 towards left Find the position and velocity of A at Ans 110 cm away from the edge 230 cm s towards right Fig 1 56 t 1 s A 200 cm B

19 Two blocks each having a mass M rest on frictionless surfaces as shown in the figure If the pulleys are light and frictionless and M on the incline is allowed to move down then the tension in the string will be a Mg sin 8 b Mg sin 8 c M Mg sin e 2 M d 2Mg sin e 20

An elevator car lift is moving upward with uniform acceleration of 2 m s At the instant when its velocity is 2 m s upwards a ball is thrown upward from its floor The ball strikes back the floor 2 s after its projection Find the velocity of projection of the ball relative to the lift A 10 m s B 10 m s C 12 m s D 12 m s

doard Competitive Exams Level Laws of Motion 13 An Olympic diver dives off the high diving platform The magnitude of his momentum will be a maximum at point t 100 NS 3 1000 Ns What is the magnitude of the impulse of force shown in the following figure F N 100 3 900 NS b 1 2 b 4 d 40N 10 What is the impulse of force shown in the following figure FN 10 2 900 NS 4 1100NS FU 22 450 S 11 Acricket se caches a ball of mass 100 g mowing with a speed of 25 ms fite tel scaught in the average of the tow exerted on the hands of the plas

oy truck of mass Mis moving towards left with an acceleration a as shown in figure 2 17 It is connected to a mass m with a massless and frictionless string going over a movable massless pulley to which another mass m is connected Find the force acting on the truck towards right and the accelerations of masses m and m F4 m m

0 13 The value of IT T l in the given diagram is 30 T 60 3 T 10 kg 1 200 3 1 3 2003 11 7 5 kg 200 2 3 1 4 2006 3 1

The guy wires AB and AC are attached to the top of the transmission tower The tension in cable AB is 8 5 kN Determine the required tension Tin cable AC such that the net effect of the two cables is a downward force at point A Determine the magnitude R of this downward force Assume a 42 m b 49 m c 34 m and d 42 m Answers R XXI LAL

4 In the given figure the string has mass 4 5 g Find the time taken by a transverse pulse produced at the f to reach the pulley g 10 ms 2 ZE A wave moves with speed 300 ms 1 on 25cm 2kg 2 m mmm floor ALLEN CHAPONAR

A uniform rope is suspended vertically from a point such that its lower end just touches a horizontal table Now the rope is released from the point of suspension Prove that when I part of the rope touches the table force applied on the table equals the weight of length 31 of the rope Let p mass per unit length of the rope

A particle moves along a straight line with a retardation of aun 1 where v is the velocity at time t and a is a positive constant If at t 0 the velocity of the particle 1 is u show that at nun un

Regular Medical 2020 22 A 5 kg block rests on horizontal surface Which of the following option is incorrect g 10 m s 5 kg TTT TI 1 The normal force on the block equals its weight because of Newton s second law 26 2 The normal force on the block is equal to the weight not because of Newton s third law 3 The normal force on the block equals its weight because of Newton s third law 4 The normal force on the block is 50 N

If linear momentum of particle changes with time t as p 32 2t 1 kgm s then force acting on particle at t 3 s will be NCERT Pg 95 1 10 N 3 15 N 2 20 N 4 11 N ar re ro th 1

8N 1 2Kg 4Kg TI Smooth From the given figure find contact forc between blocks of 2 kg 4 kg 4 2 1m 20 N TITI 8 3 Zero 4 20 3

Ne In the following arrangement the system is initially at rest The 5 kg block is no the pulleys and string to be massless and smooth the acceleration of block B Ska 100 C a D 2

astration 1 Two masses m 3kg and m 4kg are connected to the two free ends of an inextensible string which passes over a frictionless pulley suspended by an inextensible string to a rigid support as shown in fig Calculate i the acceleration of the system ii tension in the string used for connecting the masses and iii the tension in the string used for suspending the pulley m 4kg L m 3

Same spring is attached with 2 kg 3 kg and 1 kg blocks in three different cases If X X2 X3 be the extensions in the three cases then o elle e 2 kg 1 X X X3 3 X3 X X elle 2 kg 3 kg o relle 2 kg 1 kg 2 X X X3 4 X 0 X3 X 2 kg

3 At t 0 a stone of mass 10 gm is thrown straight up from the ground level with a speed 10 m s After 1 s a second stone of the same mass is thrown from the same position with a speed 20 m s What is the position of the first stone from the ground level at that moment Take g 10m s DUMET 2010 a 10 m c 2m b 1 m d 5 m

9 Let F 30 N and the slope be frictionless Determine the force between the 2 boxes 3K 2kg

omprehension Q 7 to Q 9 Sound sources S and S are located at x and x respectively The sources produce tones with the same phase and amplitude The frequency can be varied from 175 Hz to 625 Hz but both speakers have the same frequency Assume that the pressure variation amplitude po does not decrease with distance from the source Use 340 m s for the velocity of sound in air and x 0 850 m y4 A p 2p cos 2nft sin 2TX 2 S Xo Both S S emit sound of frequency 300 Hz and a detector is moved along x axis How many minima will the detector observe in going from S S A 6 B 4 C 8 D 10 For which frequencies in the above range is minimum sound intensity heard at all points along the x axis with x Xo A 200 500 Hz B 300 500 Hz C 300 400 Hz D 200 400 Hz Consider the region on the x axis between the two sound sources S and S Which of the following equations is the correct equation for the resultant sound wave pressure for all points between S and S on x axis B p 2po sin 2nft cos 2TX C p 2p sin 2nft cos X0 X D None of these 2TX 32

The spring mass system shown in the figure is in equilibrium at rest If the mass is pushed up by a distance mg 2k and released its instantaneous acceleration will be A g B 2g C g 2 D zero m

Two blocks of masses 2 kg and 4 kg are hanging with the help of massless string passing over an idea pulley inside an elevator The elevator is moving upward with an acceleration The tension in th string connected between the blocks will b Take g 10 m s g 2 1 40 N 3 80 N 6 2 60 N 4 20 N

1 A block of mass m slides on a circular track of radius r whose wall and floor both have coefficient of kinetic friction with the block The size of block is small compared to the radius of the track The floor lies in horizontal plane and the wall is vertical The block is in contact with both wall and the floor The block has initial speed v For the block to circle the track exactly once before coming to rest vo is given by gr e 1 Find the value of K

arrangement shown in Fig 6 337 at a particular instant the roller is coming down with a speed of 12 ms and C is moving up with 4 ms At the same instant it is also known that w r t pulley P block A is moving down with speed 3 ms Determine the motion of block B velocity w r t ground a 4 ms in downward direction b 3 ms in upward direction c 7 ms in downward direction 12 ms C A B 14 ms Fig 6 337

A mass M is suspended as shown in Fig 6 384 The system is in equilibrium Assume pulleys to be massless K is the force constant of the spring Lower support el A K B A M Fig 6 384 44 The extension produced in the spring is given by a 4Mg K b Mg K c 2Mg K d 3Mg K 45 Find the net tension force acting on the lower support b 2Mg Le 3Mg d 4Mg a Mg 46 If each of the pullies A and B has mass M then find the net tension force acting on the lower support Assume pulleys to be frictionless

22 A platform of mass m and counterweight of M m where M 3 m are connected by a light cord which passes over two smooth pulleys see figure A man of mass M is standing on the platform which is at rest If the man leaps vertically upwards and out of platform with velocity 10 ms find the distance through which the platform will descend a 1 m c 3 m Mm M m b 2 m d 4 m

12 A staircase contains three steps each 10 cm high and 20 cm wide figure 3 E9 What should be the minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane Figure 3 E9

3 45 35 What is the maximum value of the force F such that the block shown in the arrangement is just about to move F 60 1 20 N 2 10 N 3 12 N m 3 kg 1 2 3

Two men P Q of masses M and m M hold a light rope passing over a smooth fixed pulley F and Q climb up the rope so that the acceleration of Q upward is double that of P downward The tension in the rope is 2Mm A 8 C M m 3Mm 2 M m g B D 3Mm M 2m 3Mm 2M m 8 g

Force acting on a body varies with time as shown below If initial momentum of the body is p then the time taken by the body to retain its momentum p again is 1 8 s 3 6s in N F 1 2 4 t sec 2 4 2 2 s 4 Can never obtain

8 Two boys are standing at the ends A and B of a ground where AB a The boy at B starts running in a direction perpendicular to AB with velocity v The boy at A starts running simultaneously with velocity v and catches the other in a time t where t is v Vit a a x 2 c V V A b d a v vj 2 a 2 V

3 5 5 m s 4 4 8 m s Which are of the following represents uniformly acceleated motion Os t alo 2 x b 1 Far 6 1 X t a b x a b 3 t 4 x t a se art te bos bruop A particle experiences a constant acceleration for

A block of mass 5 kg is sliding down a smooth inclined plane as shown The spring arranged near the bottom of the inclined plane has a force constant 600 N m Find the compres sion in the spring at the moment the velocity of the block is maximum 5m 4m 15 cm 2 10 cm 3m 3 15 cm 4 25 cm

Two weights A and B of 5 kg and 10 kg respectively are sliding down the inclined plane as shown What is the acceleration with which the weights will slide down A 0 0 g C 0 50 g B 0 3 g D 0 866 g 4 8 30

Two weights w and we are connected by a light thread which passes over a light smooth pulley If the pulley is raised with an acceleration equal to that due to gravity then the tension in the thread will be

5 A body starts moving in a straight line under the 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 given F t graph 1 2 2 2 sec 3 4 sec F in N t sec 2 2 2 sec 4 2 2 sec

A window of weight w is supported by two strings passing over two smooth pulleys in the frame of the window in which window just fits in the other ends of the string being attached to weights each equal to half the weight of the window One thread breaks and the window moves down Find acceleration of the window if u is the coefficient of friction and a is the height and b the breadth of the window w 2 W w 2

27 In which of the following cases is the contact force between A and B is maximum m mg 1 kg A B C 30 N A B 12 N A B B a 2m s

A ball projected from ground vertically upward is at same height at time t and t The speed of projection of ball is Neglect the effect of air resistance 1 g t t 3 g t t 2 2 g t t 2 4 g t t

Three blocks of masses 6 kg 9 kg 10 kg are attached as shown in Fig 2 48 Coefficient of friction between the table and the 10 kg block is 0 2 What is the acceleration of the system What are the tensions in the two strings 10 kg 6 kg 9 kg Fig 2 48 0 392 m s 2 61 15 N 84 67 N

A rocket is fired vertically up with net acceleration of 2 After 10 second the fuel got exhausted 5 Maximum height from the ground upto which the ocket goes is Take g 10 m s 1 200 m 2 325 m 3 375 m 4 425 m

Two blocks of masses 4 kg and 10 kg are connected with a massless string and a massless spring in between them String goes over a massless and frictionless pulley as shown in figure Initially the spring is unstretched When 4 kg block is released from rest minimum normal contact force between 10 kg block and the surface in contact with it will be Take g 10 m s

on a smooth horizontal surface Two horizontal force F and 2F are applied on the blocks A and B respectively as shown in figure The block A does not slide on block B A F m 30 2 F m Then the normal reaction acting between the two blocks is 1 F 2 3 B F 3 2F 4 3F 221

Main thrust in physics is on 1 Unification 2 Reduction 3 Both 1 2

15 Two identical bodies are allowed to fall from different heights h h The ratio of their momentum 15 when they reach the ground will be hi C h A h h B h h D 1 Bago n xxh

d 16 66 N 0 866 N 36 A block of mass m is resting on a smooth horizontal surface One end of a uniform rope of mass FFR is fixed to the block which is pulled in the horizontal direction by applying a force F at the other end The tension in the middle of the rope is Kerala EEE 2009 a In 7 F b F d F F tic

57 A monkey is climbing on the rope as shown in figure The string and the pulley are light The acceleration of monkey relative to rope is 2m s downwards The acceleration of the monkey is 1 11 2 ad m s 3 5m s 15Kg 15Kg A 2 6m s 4 zero

A wire is bent in the form of an equilateral triangle PQR of side 10 cm and carries current of 5 0 A It is placed in a magnetic field B of magnitude 2 0 T directed perpendicularly to the plane of the loop Find the forces on the three sides of the triangle

A car starts from rest at time t 0 and its a t graph is shown in figure A coin is initially at rest on the floor of the car At t 1 s the coin begins to slip and it stops slipping at t 3 s The coefficient static friction between the floor and the coin is g 10 m s a m s 8 1 2 3 11 1 1 b t s