Newton's law of motion Questions and Answers

is equal to initial linear momentum of the system 13 If both the blocks moving with constant acceleration then extension in spring 32 N 1 6 cm 2 12 cm 3 3 cm 4 2 cm 7 kg K 1000 N m 3 kg 72 N

1 Rohan and Anirban are students of the same school that is 18 km away from their hostel One day they started from their hostel at the same time with an initial velocity of 29 8 km h At this speed it would take 20 min for them to reach the school on time After 5 min Rohan stopped due to some problem in his cycle Anirban didn t wait for him and moved forward Rohan took another 5 min to repair his cycle He again started with the same initial velocity as he started from the hostel Read the passage carefully and answer the following questions i What value is not shown by Anirban ii At what distance from their hostel did Rohan stop ii What is the required acceleration for Rohan to reach his school on time when he started the second time

Medical IT JEE Foundation 5 A person is standing at the floor of lift drops a coin The coin reaches the floor of lift in time t if elevator is stationary and in time t if it is moving uniformly then 1 1 1 2 1 1

7 The velocity v of a particle moving on a straight line as a function of time t is given as v v gt ff where vo g and fare constants If the particle starts from origin then its displacement just after t 1 s is stion paper 3 g 2 v g f 4 2a 3f

In trolley string arrangement a painter is holding string in hands and keeps in equilibrium the entire arrangement Mass of painter is 60 kg and mass of trolley is 20 kg What is normal force exerted by trolley floor on painter g 9 8 m s 5 1 196 N M m 2 392 N

Marks 4 1 Two blocks are connected by a spring The combination is suspended at rest from a string attatched to the ceiling as shown in the figure The string breaks suddenly Immediately after the string breaks what is the initial downward acceleration of the upper block of mass 2m 2m m m O

A cylinder of mass M length L and radius R has two cords wound around it with their ends attached to the ceiling as shown in the figure The cylinder is held horizontally with the two cords vertical When the system is released from rest the linear acceleration of the cylinder as it falls will be R A O 93 2g 3 3g 2

A particle of mass 2 kg is moving in XY plane in a circular path of radius 3m with constant angular speed 5rad s The motion of the particle is being observed from a car moving with acceleration d 31 4k m s Then the D None of these magnitude of centrifugal force F acting on the particle is A 150N B 0 F 10N C 0 F 6N A block is at rest on a rough inclined plane

37 A bubble is at the bottom of the lake of depth h A the bubble comes to sea level its radius increase to three times If atmospheric pressure is equal 1 metre of water column then h is equal to HT 261 2 1 3 251 4 301

9 It is difficult to drag a box of same mass kept in position A than in position B as shown in the picture given below A B 1 It is easier to move a box A than box B with same area of contact 5 kg 10 kg

A car weighs 1800 kg The distance between its front axle and back axle is 1 8 m Its centre of gravity is 1 05 m behind front axle The force exerted by level ground on front wheels is g 10 ms 2 NCERT Pg 178 1 7500 N 2 6500 N 3 9500 N 4 1800 N

4 In a legend the hero kid kicked a toy pig so that it is projected with a speed greater than that of its cry If the weight of the toy pig is assumed to be 5 kg and the time of contact 0 01 sec the force with which the hero kid kicked him was Speed of cry 330 m s

Calculate the acceleration of the block and trolly system shown in the figure The coefficient of kinetic friction between the trolly and the surface is 0 05 g 10 m s mass of the string is negligible and no other friction exists Trolly 10 kg O O 1 1 00 m s 2 1 25 m s 3 1 50 m s 4 1 66 m s 2 kg Block

In the situation shown in the figure the system is in equilibrium All the strings spring and pulley are light Just after cutting the string AB then the tension in string GH is N Take g 10 ms H 1 kg 5 kg 0000 B F E 1 kg D 2 kg A

8 Three objects are connected by ropes on a frictionless floor as 20N a 1Kg 0 O 3Kg a Find T b Find acceleration on 3kg c Find n on 3kg d Find the net force on 3kg block a 5 4Kg 4N ngure then

1 2 Two blocks 1 and 2 of equal mass hang from the massless frictionless pulley system in Figure 1 i If block 2 is displaced by Ay2 what is the displacement Ay1 of block 1 If block 2 moves with velocity v2 with what velocity v1 does block 1 move ii If block 2 moves downward a distance Ah2 What is the corresponding change in the potentia energy AU of the two block system in terms of m g and Ah

1 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 The masses of the pulley and the thread are negligible The friction is absent Find the acceleration of the wedge M a M

9 A bar of mass m is pulled by means of a thread up an inclined plane forming an angle a with the horizontal Fig 1 13 The coef ficient of friction is equal to k Find the angle which the must form with the inclined plane for the tension of the thread to be minimum What is it equal to thread ohit Go Ta Fig 1 13

m Two masses m and are connected at the two ends of 2 a massless rigid rod of length 7 The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod mass system see figure Because of torsional constant k the restoring toruque is t k0 for angular displacement 0 If the rod is rotated by 0 and released the tension in it when it passes through its mean position will be 1 2 3k0 1 m 2 LU 2 m 2k0 1

A mass of 1 kg is suspended by a thread It is lifted up with an acceleration of 4 9 m s 2 and then lowered with an acceleration of 4 9 m s2 The ratio of tensions in first case to second cases is g 9 8 ms 2 1 O 1 1 3 1 1 3

The system shown in figure is in equilibrium Masses m and m are 2 kg and 2 5 kg respectively Spring constants K K and K are 200 Nm 1000 Nm 500 Nm respectively If the elongation in spring A is 20 cm and the compression in spring C is 1 cm then find out the elongation in spring B in cm K Imm m K K

Solvelancer Test A and starts from rest and moves with acceleration ratio 49 If dince covered by A is 25 of distance covered by then find the ratio of time required by and A Solvelancer Test n 3 4 6 4 3 c 2 3 d 3 2 a b d

Bullets of 0 03 kg mass each hit a plate at a rate of 200 bullets per second with velocity of 50 m s and reflect back with velocity of 30 m s The average force acting on the plate in newton is 120 180 480 245

A pendulum is hanging from the ceiling of a If the cage moves up with constant acceleration a its tension is T and if it moves down with same acceleration the corresponding tension is T 2 The tension in the string if the cage moves horizontally with same acceleration a is AS C 44442 T T T 2 T T 2 a T B D T a T T2 2 T T2 2

Block 1 sits on top of block 2 Both of them have a mass of 1 kg The coefficients of friction between blocks 1 and 2 are 0 75 and 0 60 The table is frictionless A force P 2 is applied on block 1 to the left and force P on block 2 to the right Obtain the minimum value such that both blocks move relative to each other and fill P 2 in OMR of P P min min P 2 1 2

NS Two blocks each having a mass M rest on frictionless surface 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 2 3 Mg sin 0 Mg S sin 0 B Mg sin 0 x1 2 D 2 Mg sin 0 66 lirts 126

The flatbed truck starts from rest on a road whose constant radius of curvature is 30 m and whose bank angle is 10 If the constant forward acceleration of the truck is 2 m s2 determine the time t after the start of motion at which the crate on the bed begins to slide The coefficient of static friction between the crate and truck bed is us 0 3 and the truck motion occurs in a horizontal plane 10

Assertion Mass is a measure of inertia of the body in linear motion Reason Greater the mass greater is the force required to change its state of rest or motion a Both assertion and reason are true and reason is the correct explanation of assertion b Both assertion and reason are true but reason is not the correct explanation of assertion c Assertion is true but reason is false Both Assertion and Reason are false

Figure shows two blocks A and B are connected through pulley and spring system Block A on a frictionless surface has a mass of 2 Kg Block B suspended by cables has a mass of 3 Kg The spring has a stiffness of k 500 N m and an unstretched length of 400 mm the system is released from rest in the position shown x 800 mm The speed of the block A rounded off to the nearest higher integer in m s when x 0 mm is g 10 m s 600 mm www K 500 N m 3kg B

A man of mass m has fallen into a ditch of width d Two of his friends are slowly pulling him out using a light rope and two fixed pulleys as shown in the figure Both the friends exert forces of equal magnitude F When the man is at a depth h the value of F is mg 4h A 4h C mgd h B mgh d D infinite h d

Match the following two column for a convex lens corresponding to object posi Note O Optical centre F First focus F Second focus Column l Column II p Real A Between O and F B Between F and 2F C Between O and F D Between F and 2F Aa shown in Colum JEE FOLLO s Inverted

Sand is being dropped from stationary hopper at the rate of 5 kg s on to a conveyor belt moving with a constant speed of 2 m s What is the power delivered by the motor drawing the belt A 10 watts C 30 watts B 20 watts D 40 watts du

A ball of mass 10 kg moving with a velocity 10 3 m s along the x axis hits another ball of mass 20 kg which is at rest After the collision first ball comes to rest while the second ball disintegrates into two equal pieces On piece starts moving along y axis with a speed of 10 m s The second piece starts moving at an angle of 30 with respect to the x axis The velocity of the ball moving at 30 with x axis is x m s The configuration of pieces afte collision is shown in the figure below The value of x to the nearest integer is y axis Piece 1 v 10 m s 30 Answer x axis

A uniform rod of mass M pulled by force F on smooth surface The value of tension T in the rod varies with the distance X from the force end is according to the graph 1 3 TA TA X P X 2 4 TA TA F X

A force gives an object of m an acceleration of 12 m s and an object of mass m an acceleration of 10 m s The ratio of accelerations the force would give to an object of mass m m and m m 1 4 1 3 10 1 2 2 1 4 11 1

An object of mass 500g initially at rest is acted upon by a variable force whose X component varies with x in the manner shown The velocities of the object at point X 8 m and X 12 m would be the respective values of nearly F N 20 10 10 20 25 77 458 10 12 1 18 m s and 24 4 m s 2 23 m s and 24 4 m s 3 23 m s and 20 6 m s 4 18 m s and 20 6 m s x m

For a short period of time the frictional driving force acting on the wheels of the 2 6 Mg van is I 6002 N where is in seconds Figure 1 igure V 1 of 1 Part A If the van has a speed of 18 km h when 0 determine its speed when 5 s Express your answer to three significant figures and include the appropriate units v 4 99 Submit m S Previous Answers Request Answer Incorrect Try Again 4 attempts remaining

cylindrical region of radius 10 cm as shown in figure A uniform wire of length 80 cm and resistance 4 0 2 is bent into a square frame and is placed with one side along a diameter of the cylindrical region If the magnetic field increases at a constant rate of 0 010 T s find the current induced in the frame a X X 1 3 9 105 A 2 0 2 x 105 A 3 08 10 5 A 4 10 x 105 A Xx X X X X X X X X b X X d

Find out the value of T in the given diagram 1 12 N 37 2 8 N 3 6 N 4 3 N 35 37 1 12 N 2 8 N 3 6 N

7 1 50 N 2 25 N 3 500 N 4 10 N Three blocks with masses m 2m and 3m are connected by strings as shown in the figure After an upward force F is applied on block m the masses move upward at constant speed v What is the net force on the block of mass 2m g is the acceleration due to gravity 1 Zero 2 2 mg 3 3 mg 4 6 mg AF m 2m 3m T 27 1 50 N 2 25 N 3 dia i fanger va BRI E T m 2m 3m m 3 3 fanda Torta calu 1 Zero 2 2 mg 3 3 mg 4 6 mg Gia Er 2n F m 2m 3m

5 A particle of mass m 1 kg is lying at rest on x axis experiences a net force given by I F x 3x 2 Newton where x is the x coordinate of the particle in meters The magnitude of minim velocity in negative x direction to be imparted to the particle placed at x 4 meters such that it read P P V27 m s Find the value of 1300 the origin is

A string of length L and mass M is lying on a 40 horizontal table A force F is applied at one of its ends Tension in the string at a distance y from the end at which the force is applied is 1 zero 2 F 3 4 F L Y L F L Y M A 1 2 F 3 4 F L Y L F L Y M de y

A person of mass 60 kg is inside a lift of mass 940 kg 37 and press the button on control panel then lift starts moving up with an acceleration 1 0 metre per second square if g is equal to 10 metre per second square the tension in the supporting cable is 1 8600 N 2 9680 N 3 11000 N 4 1200 N 60 kg 94 fan for an add a Haus derd fa g 10 af farz ach ted 1 8600 N 2 9680 N 3 11000 N 4 1200 N

In the arrangement shown the pulleys are fixed 30 and ideal the strings are light m m and S is a spring balance which is itself massless The reading of S in unit of mass is S m 1 m m 3 m1m2 m m m 2 m 2m m2 m m fa 314 m m 3 fa 1 m m fe enrer z HER fer s m1m2 m m GHE S 2 4

The diagram below shows the horizontal forces 33 af 20 0 kg on a 20 0 kg mass The force are constant in time If the mass starts from rest how far has it traveled in the horizontal direction after 3 00s 70 0N 100 0N 1 4 50 m 2 6 75 m 3 9 00 m 4 25 5 m 20 0 kg GO FORTHERN grund af fem fandt and 70 0N 100 0 1 4 50 m 2 6 75 m 3 9 00 m 4 25 5 m 20 0 kg

ALLEN A train has 10 wagons each of mass 1000 kg 34 attached to it They are being pulled by force 10 N Find out force exerted on last four wagons 1 4 10 N 2 4 10 N 3 5 10 N 4 5 10 N test for 10 of 1000 kg 10 N 1 4 10 N 2 4 10 N 3 5 10 N 4 5 10 N

4 6 mg Two blocks of masses 2 kg and 1 kg are in 28 contact with each other on a frictionless table When a horizontal force of 3 N is applied to the block of mass 2 kg the value of the force of contact between the two blocks is 1 4N 3 5N 2 3N 4 IN 4 6 mg for the 2 kg 1 CH CH TET HUY m HUB J EN CHRIF 1 4N 3 5N 2 3M 4 IN

1 3 n m m m m m Two blocks each of mass M are placed on a 31 smooth inclined plane as shown in figure Then M M B 160 30 1 block A moves down the plane 2 block B moves down the plane 3 both the blocks remains at rest 4 None of the above 3 1 2 3 4 m m at action uch fa fa facrI TRI DE M At site and B site and art

43 A 0 5 kg ball moving with a speed of 12 m s strikes a hard wall at an angle of 30 with the wall It is reflected with the same speed and at the same angle If the ball is in contact with the wall for 0 25 seconds the average force acting on the wall is 30 30 1 48 N 2 24 N 3 12 N 4 96 N If the blocks are placed on smooth plane as 44 0 5 kg 12 m s f 30 a and af da d at da 30 30 1 48 N 2 24 N 3 12 N faut

Apparent weight of a man of mass 50 kg in a lift 41 is 600 N Lift is accelerating upward Calculate acceleration of lift 1 3m s 2 2 5m s 3 Im s 4 2m s 50 kg 600 N fa fa 1 3m s 2 2 5m s 3 1m s2 4 2m s