Newton's law of motion Questions and Answers

33 A ballon of weight W is falling vertically 33 downward with a constant acceleration a g The magnitude of the force the air resistance is 1 W 2 W 1 5 3 W 1 4 W 50 of a g at any 1 W 3 W 1 2 W 1 4 W g

3 1 A ball is dropped from a height of 20cm above the water surface of a lake Refractive index of water A fish situated below the surface of water along the path of motion of the ball is observing the ball When the ball reaches a depth of 12 8cm from the surface of water then what will be the valocity of the hall relative to the fish

ALLEN 35 According to given figure monkey X of mass 35 funk 15 kg moving downwards with acceleration 2 m s and monkey Y of mass 10 kg is moving upwards with acceleration 1 m sec on light rope then find out force exerted on point O 1 210 N 2 230 N 3 21 N 4 200 N 2 m s 15 kg 10 kg m s 3 2 m s rafa a 10 kg Y I m sec 1 210 N 2 230 N 3 21 N 4 200 N 2 m s 0 10 kg 15 kg m s

A terrorist places a bomb at a horizontal distance of 6 m from the foot of building of height 8 m When the bomb explodes its fragments fly in all directions with a velocity upto 20 m s Find how long a man on the top of the building will be in danger g 10 m s

A person of mass 60 kg is inside a lift of mass 940 kg and presses the button on control panel The lift starts moving upwards with acceleration 1 0 ms 2 If g 10 ms the tension in the supporting cable 8600 N 9680 N 11000 N 1200 N

Starting from rest a car moves with a constant acceleration and comes to a momentary stop with the same nstant deceleration Subsequently it reverses its motion and returns to its original position in a similar manner hich one of the following graphs of momentum p versus time t best describes the motion of the car P MU P A HEN A const vist Muss der your 1 on 13e ve RE M D 11 u W

5 A solid block of mass 2 kg is resting inside a cube as shown in the figure The cube is moving with the velocity v 5ti 21 m s t is time in second The block is at rest with respect to the cube and coefficient of friction between the surfaces of cube and the block is 2 Then g 10 m s a force of friction acting on the block is 10 N b force of friction acting on the block is 4 N c the total force exerted by the block on the cube is 14 N d the total force exerted by the block on the cube is 20 5 N

3 1 92 unit 4 0 96 unit 32 A uniform ladder of mass m 40 kg rests against a smooth vertical wall making an angle 30 with horizontal The lower end of ladder rests on a rough floor having An electrician having 22 mass 80 kg attempt to climb the ladder to repair house wiring Fraction of length than can be encountered by the electrician before the ladder begins to slip will be 112 114 2 1 Medical

38 Ends of a thin uniform inextensible rope of mass m 1 0 kg and length 1 2 0 m are fastened to the ceiling close to each other If one of the ends is released and allowed to fall freely as shown in the figure find the largest force that the fastening at the other end must be capable of bearing so that rope remains fastened there Acceleration of free fall is g 10 m s

2002 A A block of mass 5 kg is hanging over an ideal pulley through a string ideal The other end of the string is pulled by a constant force F such that the kinetic energy of the block increases by 5 J in 1s If the block is pulled from rest then take g 10 m s 1 Tension in the string is 50 N 2 Work done by F is 5 J in 1s 3 Work done by gravity on block in 1s is 5J 4 Tension in the string is 57 07 N

41 A hemisphere of radius R and of mass 4m is at rest on a smooth horizontal surface as shown in the figure A small particle of mass m is released from rest at the top of the hemisphere The angular velocity of the particle relative to centre of hemisphere at an angular displacement 8 when velocity of hemisphere is v would be m 1 2 3 4 5v Rcose 2v cos 0 R 3v sine R 5v Rsine R o

20 Two blocks A and B are connected with the help of ideal strings and pulleys as shown in the figure If the system is released from rest and all surfaces are smooth then acceleration of block B will be 4g 3 3g 3 2 4 kg A 7777 B 8 kg 2 4 29 3

12 A rope can with stand the 120 weight of a monkey tries to climb up along this rope The maximum acceleration of monkey on the rope such that the rope does not break is take g 10 m s 1 10 m s 2 12 m s2 3 2 m s 4 1 2 m s

Two forces whose magnitude are in the ratio 9 11 giv a resultant of 38 N If the angle of their inclination is 30 then what will be the magnitude of each force a 19 8 N 24 2 N b 20 N 24N c 25 N 30 N d None of these

the slabs from rest and have to put them on the elevated platform at a height h If the maximum tension that the cable of crane machine can tolerate is nw n 1 then minimum time in which ascent can be done by the machine is Tmin 0 1 2h n 1 g 2 n 1 2 2nh n 1 g 12h

Aakash Rank Booster Test Series for NEET 2020 Two objects A and B each of mass m are connected by a light inextensible string They are restricted to move on a frictionless ring of radius R in a vertical plane as shown in fig The objects are released from rest at the position shown Then the acceleration of mass A just after release is nearly g 10 m s A B 1 Zero 3 14 14 m s 45 2 5 m s 4 07 m s

8 7 points A crate of mass 425 kg is lifted by the hoisting mechanism shown The cable is wrapped around the pulley radius R 0 6 m and mass M 100 kg and the pulley turns without slipping If a tension of magnitude Ta 2150 N is maintained in the left hand cable what is the tension T2 in the cable attached to the crate T A 2360 N B 2140 N C 1920 N D 1730 N E 1510 N T

8 9 C 1 C 3 3C Two small blocks each of mass 2 kg are connected by an inextensible string light Blocks are placed over a fixed smooth wedge as shown in the figure and system is released from rest Magnitude of acceleration of both the blocks will be g 10 m s 1 1 m s m s 37 2 20 4 4C 90 53 2 2 m s 4 2 m s A charged particle Q is placed outside a hollow

A block of mass m hangs at rest from the calling of a stationary elevator at the end of a massless spring Minimum constant acceleration with which the lift should start moving so that the spring attains natural length at least once during the subsequent motion of the block is A g upwards B g downwards 9 C upwards g 2 downwards

A person standing on the floor of an elevator drops a coin The coin reaches the floor in time t if the elevator is at rest and in time t2 if the elevator is moving uniformly Then 1 t t or t t2 depending upon whether the lift is going up or down 2 t t 3 t t

A current carrying circular loop of radius 10 cm has a magnetic induction of 3 6 x 10 5T at its centre What is the magnetic dipole moment of the loop YOU A 150 10 Am B 180 10 Am C 160 10 Am D 145 10 Am

Two springs have force constant K and K K K Each spring is extended by same force F It their elastic potential energy are E and E then E E is K 1 K2 3 K N K u In 129 K 2 4 K K

9 A potential barrier V volts exists across P junction The thickness of the depletion region is d An electron with velocity vo approaches P junction from P side The velocity of electron crossing the junction is 1 2Ve m 2 2Ve m

Consider the diagram a and as are accelerations of two blocks respectively just after cutting the spring Similarly as and a are accelerations of two blocks just after cutting the string Which one of the following option is not correct a a g c a mg m b a g d a4 g

A spring with spring constants k when compresse by 1 cm the potential energy stored is U If it further compressed by 3 cm then change in potential energy is 1 3U 2 9U 3 8U 15U

Figure 2 64 shows a block of mass M supporting a bar of mass m through a pulley system If system is released from rest find the acceleration of block M and the tension in the strings m Figure 2 64 M

In the figure shown what should be the value of force F applied so that the whole system can remain in the state of rest Both the wedges are of the same mass M and the angle inclination is 0 Neglect friction a Mg tan 0 b Mg tan d Mgsin c 2Mgtano 20 F

Two blocks of masses 1 kg and 3 kg are connected by an inextensible string through a massless pulley as shown in figure All surfaces are smooth A ball A of mass 1 kg is moving towards block of mass 1 kg with a velocity 10 m s and collides inelastically at t 0 Consider that there will be no jump of 3 kg block at any time Now match list 1 to list 2 A P R S Codes A B When combined mass come back to its initial position string Q regain its tension then at the same moment velocity In Sl 1 kg List I The combined mass travels up the incline by a distance in Sl unit P Q R 2 3 1 1 2 T unit of block of mass 3 kg The mass 3 kg moves up to a height in Sl unit before stop Time in Sl unit taken by 3 kg block to rise up and come back to its initial position 4 30 S 4 3 kg 1 1 List II 2 0 5 3 2 4 2 5

41 A body of mass m accelerates uniformly from rest to velocity v in time interval T The instantaneous power delivered to the body as a function of time t is 1 3 mv T mv T t 2 t 2 4 mv T t mv 2 T

estion 2 Marking Sche a Zero c 2g 3 05 00 In the diagram shown the larger block is being moved with an acceleratic 2g What is the acceleration of the 2m mass block with respect to the Assume no friction Strings are ideal b 4g 3 d None Mark

In the figure shown the system is released from rest Find the velocity of block A when block B has fallen a distance Assume all pulleys to be massless and frictionless La ge C 5ge B ge D None of these Am P m B

The blocks A and B shown in the figure have masses M 5 kg and M 4 kg The system is released from rest The speed of B after A has travelled a distance 1 m along the incline is 3 A g 2 LOND g 2 3 Using work energy tworm B D 3 9 4 g 2 B 377 5m

13 A right triangular plate ABC of mass m is free to rotate in the vertical plane about a fixed horizontal axis through A It is supported by a string such that the side AB is horizontal The reaction at the support A is 1 3 mg 3 mg A 1 B 2 mg 3 4 mg 2

25 Calculate the tension in the string BC as shown 90 B 0 1 2mg cose 2 mg sine 3 2mg sine 4 mg cose 26 Calculate the tension in the string connect between the 1 kg and 3 kg masses 3 kg 1 kg

A ball falls vertically onto a floor with momentum P then bounces repeatedly The coefficient of restitution is 1 2 the total momentum imparted by the ball to the floor is 1 2P 3 3P 2 3P 4 4P

A body starts moving in a straight line under the influence of a variable force F The time after which the initial velocity of the body becomes equal to final velocity of body for the given F t graph will be F N 4 0 1 2 t sec

2 20 points Consider the following figure A ball of mass 2 kg slides from rest at the top of an inclined plane point A It collides with the box at B and together they will slide down a frictional surface to point C indicated as red surface before sliding down on another inclined plane to point D Eventually they hit a spring whose spring constant 200 N m Find the speed of the ball at B speed of ball box at C and at D Also obtain the maximum compression in the spring 2 Kg Starts from rest Friction less Initially at rest B 8 Kg 8 m Friction surface Hk 0 4 5 Friction less Friction less www

20 points An object of mass m 10 kg is moving at speed of 35 m s along positive x axis It collides with another mass m2 20 kg which is at rest Mass m breaks into two equal pieces Now all three masses travel in different directions with different speeds Mass m moves at along positive x axis with a speed of 10 m s One of the pieces of m2 moves at 5 m s making an angle 25 of counterclockwise from x axis Find the magnitude and direction of the velocity of the third piece

In a garden a spherical sprinkler is used at the end of the hose from which the speed of the flowing water is the same to every direction The water beam which is directed vertically upward reaches a height of h Once the sprinkler is placed to the ground and at another time to a height of h By wha factor will the watered area be greater in the second case Neglect air resistance and consider the pressure in the sprinkler constant A 2 1 C 7 4 B 3 2 D 3 1

1 The upper portion of an inclined plane is smooth and lower portion is rough A particle slides down from rest from the top and just comes to rest at the foot If the ratio of the smooth length to the rough length is m n the coefficient of friction is a angle of inclination 1 3 m n n m n n tana cota 2 4 m n n 1 1 201 cota

One or more than one correct answer type 4 A block of mass 10 kg is placed on rough horizontal surface as shown in the figure Ch correct statements MAQ 10 kg 0 5 H 0 4 a If F 45 N the friction on the block is 45 N and acceleration of the block is zero b If F 50 N the force of friction is 40 N and the acceleration of the block is 1 m s c If F 60 N the force of friction is 40 N and the acceleration of the block is 2 m s d If F 60 N the distance travelled by the block is 1 m in 1 s

In the figure F and F the two unknown forces give a resultant force of 80 3 Nalong the y axis It is required that F must have minimum magnitude Find the magnitudes of F and F 2 y 20

1 Find the maximum value of M m in the situation shown in figure so that the system remains at rest Friction coefficient of both the contacts is u string is massless and pulley is friction less a c m cos e sin 0 u cos 0 cos e sin 0 u cos 0 M b d 0 sin e sin 0 u cos 0 sin u cos 0

A car starts from rest and accelerates uniformly for 200m Then moves with constant speed for 160m Finally comes to rest in 50m If total time of journey is 33 sec Find time for which particle runs with constant speed

3m 2m 0 arctan 3 4 13m s 4 cm A block is placed in a groove made in the turntable having frictionless wall at 4cm from the centre of a turntable which is at rest The block fits tightly in the groove and is free to move in the groove The turntable is steadily accelerated at 2 5 rad s as shown in figure Coefficient of friction between the floor of groove and block is 0 1 The time in second at which the particle is about to slip is 7 6 When a 2 kg car driven at 20 m s on a level road is suddenly put into neutral gear i e allowed to coast the velocity decreases in the following manner The magnitude of the resistive force on a cruising plane is directly proportional to v where v is the planes velocity The power expended by the plane is P when the plane is cruising at velocity v The power 8 expended by the plane when the plane is cruising at velocity 2v is X The value of X P is When a 2 kg car driven at 20 m s on a level road is suddenly put into neutral gear i e allowed to coast the velocity decreases in V 1 A 20 F 60 t 20 where t is the time in sec The power in Watt required to drive this car at 10m s on the same road is The minimum value of F so that block is in equilibrium is xmg Value of x is m s 1 3 A 2mg C mg 2 B mg D block cannot be in equilibrium A box is sliding on smooth surface with constant speed A particle is projected inside box from point P with velocity rel 10m s with respect to box at an angle a 60 with the floor of box The particle lands at point Q in the box with respect to observer B If to an stationary observer A the horizontal displacement of particle is zero then the velocity of box V at the moment particle was projected is in m s rel a 60 B Velocity position graph of a particle is as shown in the figure The acceleration of the particle when its velocity is 6m s is in m s

4 All of the above In figure man A is standing on a movable plank while man B is standing on a stationary platform Both are pulling the string down such that the plank moves slowly up As a result of this the string slips through the hands of the men Find the ratio of length of the string that slips through the hands of A and B 1 3 2 3 4 3 2 3 4 4 2 3 faces are frictionless whil

3 A particle starts from rest with constant acceleration If first distance S is covered in time t then the time taken to cover next 2S distance is 2 3 2 t 1 2 1 t 3 3 1 t 4 8 The velocity of a swimmer in still water is vand water current in river is V2 The swimmer is applying strokes perpendicular to water current If d is width of river the time taken by the swimmer to cross river is 1 v 2 2 kg MO d PHYSICS In the given arrangement pulley and strings are ideal The force applied by pulley on the table is g 10 ms2 2 kg 3 4 15 1 10 N 2 20 N 3 10 2 N 4 20 2 N A bomb is projected with velocity v at an angle with the horizontal At maximum height it explode into two equal parts If one piece retraces its pati at what distance from point of projection othe piece with strike the ground 1 vsin 20 9 3 3 v sin 20 12 v sin 20 2g A solid sphere of mass M and radius R is concentric with a thin spherical shell of mass M and radius 2R The gravitational potential at distance x from their common centre is 2R x R 2 26 2v sin 20 9 4

Figure 2 35 shows a cylinder 4 of mass M which is resting on two smooth edges one fixed and other is that of a block of B At an instant block B is pulled toward left with a constant speed v Find the force exerted by the cylinder on the fixed edge after some time when the distance between the two edges will becom x 2 R At t 0 the distance between the two edges was zere 21 B

The block of mass m slides on a wedge of mass m which is free to move on the horizontal ground Find the accelerations of wedge and block All surfaces are smooth Let a acceleration of wedge tion of block with respect to wedge 0 E m

1 2ER 2x 4TR 1 2 C 3 5 C 3 14 In the circuit the batteries have emf E E 1V E 2 5 V and the resistance R 100 R 20 92 capacitance C 10 F The charge on the left plate of the capacitor C is R EHH E A 2 2 R www R 2V 2 4 C 4 12 C 15 A capacitor of capacitance C is charged by a battery of emfe If polarity of battery is reversed then find the heat dissipated in the circuit 1 C2 2 20 3 30 4 402 16 In the circuit shown the galvanometer shows current The value of resistance Ris 2 2TE R K mm m 12 V R ww 592 1 19 2 292 4 992 3 492 17 A block of mass m is attached to two unstretched springs of spring constants K and K as shown in figure The block is displaced towards right through a distance x and is released Find the speed of the block as it passes through the mean position shown K K 4m K mm laka Med IT JEE FO 4 18 A uniform chain of length and mass moverhangs a smooth table with its two third part lying on the table Find the kinetic energy of the chain as it completely slips off the table 1 mgl 2 mgl 2 3 mgl 4 mgl 19 A heavy stone is thrown from a cliff of height h with a speed v The stone will hit the ground with maximum speed if it is thrown 1 Vertically downward 2 Vertically upward 8 K K 2m 3 Horizontally 4 The speed does not depend on the initial direction K K m 20 A simple pendulum is oscillating with an angular amplitude 90 For what value of a the acceleration of bob will be directed horizontally UJ 200 100 3 60 4 cos 1 3 21 The potential energy U versus position x curve of spring mass system executing SHM is shown If spring constant K 2 x 10 N m and mass of the object m 2 kg then which of the following is incorrect 2 45 x m 1 K 200 J 2 Amplitude 10 cm 3 Maximum velocity 10 m s 4 Maximum acceleration 10 m s