Newton's law of motion Questions and Answers

metallic rod rotates about its perpendicular bisector with constant angular speed If it is heated uniformly to raise its temperature slightly NCERT XI II 277 1 its speed of rotation increases 2 its speed of rotation decreases 3 its speed of rotation remains same 2 mp 12 4 its speed increases because its moment of inertia increases Jew

A DLOCK OT mass M is attached with a roa or mass M and lengtn L A norizontal Torce F is appuea on its ena I ne friction is abser correct statements are 000 M M F Tension at the mid point of rod is 3F Tension at a distance from block is Tension is same through out the rod F The force applied block on rod 1

5 The moveable bracket shown may be placed at any height on the 3 cm diameter pipe If the coefficient of friction between the pipe and bracket is 0 25 determine the minimum distance x at which the load can be supported Neglect the weight of the bracket 6 cm W

Let in a given time displacement of A is x of B is x and that of y is x in downward direction As the length of string will remain constant so we can write x x x x3 x x x 0 2x 2x x3 0 a Differentiating we get 2v 2v V3 0 2v 2 1 2 0 v 0 b Again differentiating we get 2a 2a a3 0 2a 2 3 1 0 a 7 2 ms 2 V VB 5 V 10 2 2 VA 20 8 a Vp V 0 V 30 ms 1 X34 B Y A

A string of mass 0 2 kg and length 2m is tied at two ends to fixed supports under a tension of 10 N A point P on the string is found to travel from one extreme to other in 0 1s Taking one end as x 0 and the other end x 2 m and t 0 as the time when P is at rest Position of P is x The correct statements will be Multiple Correct Type 1 For 0 t 0 1s energy flows across P in positive x direction for 0 x 1 m 2 For 0 t 0 05 s energy flows across P in negative x direction for 0 x 1m 3 At t 0 05 s rate of energy flow through P is zero for x 0 5 m 4 At t 0 1s rate of energy flow through P for all values of x is zero

The diagram shows a uniform metre rule PQ in equilibrium R P 50 N 10 cm pivot 40 cm 50 The distance PQ is 100 cm The mass of the metre rule is 0 12 kg and its weight is W a On the diagram draw and label 1 an arrow to show the force W acting on PQ at the centre of mass 2 an arrow to show the force R acting on PQ at the pivot 0 12 1 2 N b By taking moments about the pivot polgulats

3 76 A has a mass 15 kg and B has a mass of 45 kg They are on a rotating surface and are connected by a cord passing around the frictionless pulley as shown in the figure 3 134 If the coefficient of friction between the masses and the surface if 0 25 1 Determine the value of at which radial sliding will occur ii Determine how much work is done by an agent to get this angular velocity when sliding just starts 300 mm A 450 mm Figure 3 134 B

A block with mass m 2 5 kg is placed on an inclined plane with slope angle a 30 and is connected to a second hanging block with mass m by a cord passing over a small frictionless pulley as shown in the figure below The coefficient of kinetic friction k is 0 2 Find the smallest mass m for which m moves up the plane at a constant speed once it is set in motion The angle of the inclined slope is a F ma f N g 9 80 m s mi x T T m

Q 13 MULTIPLE CHOICE A board of mass m is placed on a frictionless fixed inclined plane that makes an angle 8 37 with the horizontal A block of same mass is placed on the board and is given quick push up the board with initial velocity v 8 m s The board does not move relative to the plane m 4w4a y atd at yg adusta Tiga Kaa a 2 ug da fa 37 u Affa ga 1 aga zwga ych ich ch G am mrfucv 8 m s 2 33 auf ucha a id a m 37 m V Acceleration of centre of mass of system comprising of board and block is 12 m s as a ch Agiu whia Ru 12 m s B m s cha 24 m s Magnitude of acceleration of block is 24 C The distance d covered by the block by the time its velocity drops to v 2 is 2 metre M SA v 2 ach ch s 999 92 au 2 Correct Answer D block and board is mgsin37 och am af feq qdu da c ukmgsin37 Magnitude of friction force between

A man crosses the river perpendicular to river flow in time t and travels an equal distance down the stream in time T The ratio of man s speed in still water to the speed of river will be T 1 7 12 2 7 1 7 12 12 2 7

Figure shows a wooden block on a horizontal plane at rest being acted upon by three forces F 10 N F2 2N and friction If F is removed the resultant force acting on the block will be Question Type Single Correct Type 1 2 3 F 2 N towards left 2 N towards right ON F

1 A uniform metallic rod rotates about its perpendicular bisector with constant angular speed If it is heated uniformly to raise its temperature slightly 1 its speed of rotation increases 2 its speed of rotation decreases 3 its speed of rotation remains same 4 its speed increases because its moment of inertia increases

A body floats in a liquid contained in a beaker The whole system is shown in figure falling under gravity The up thrust on the body due to liquid is zero CORRECT ANSWER

26 A 4 0 kg object moving to the right with speed 1 0 m s experiences the force shown below What are the object s speed and direction after the force ends F N 2 0 2 51 1 25 m s to the right 1 25 m s to the left O2 50 m s to the right O 2 50 to the left O 1 00 m s to the right t s

37 The acceleration of block B is Assuming pulley and strings are light ar frictionless g m A B 2 2m Smooth 2g

The elevator shown in figure is descending with an acceleration of 2 m s2 The mass of the block A is 0 5 kg The force exerted by the block A on the bla is 2 3 rrect Answer 2 2N 4 N 6 N 8 N D 2 ms

B m 9 A uniform massless spring if extended or compressed distance between every two consecutive turns pitch changes by the same amount A spring obeying this property and Hooke s law is called a linear spring a A linear spring of relaxed length lo 30 cm is attached at one end to a wall If the other end is pulled away from the wall with a force F 60 N p 6th turn from the wall reaches a position where 8th turn of relaxed spring was Find force constant of the spring b The ends A and B of a linear spring of relaxed length lo are so pulled that the ends shift by distances AlA 5 cm and AlB 25 cm as shown in the figure Find shift of a point of the spring that was at a distance lo n n 3 from the end A in relaxed spring

A collision between three balls of clay The three hit simultaneously and stick together and move as on object What are the speed and direction of the resulting blob of clay 40 g 4 0 m s 45 Select one O a Speed 0 85 m s and direction 72 below the x axis O b Speed 2 25 m s and direction 70 below the x axis C Speed 0 55 m s and direction 75 below the x axis d Speed 1 5 m s and direction 78 below the x axis 3 0 m s 2 0 m s 20 g 30 g

You swing a bat and hit a heavy box with a force of 1500 N The force the box exerts on the bat is Select one a exactly 1500 N only if the box does not move b greater than 1500 N if the box moves c less than 1500 N if the box moves Od exactly 1500 N whether or not the box moves

A small glider is coasting horizontally when suddenly a very heavy piece of cargo falls out of the bottom of the plane You can neglect air resistance What happens just after the cargo has fallen out Select one a the cargo slows down but the plane does not change speed b the plane speeds up but the cargo does not change speed c the plane speeds up and the cargo slows down d neither the cargo nor the plane change speed

5 Two weights of 15 kg each are attached by means of two strings to the two ends of a spring balance as shown in the diagram The pulleys are frictionless The reading of the balance would be www cionari 15kg 15kg 1 zero 2 15 kg 3 30 kg 4 75 kg

6 A stationary body explodes into two fragments of masses m and m If momentum of one fragment is p the energy released in explosion is p rigt a p 2 m m 2 m m 2 p m m p m m 2m m m m woj b d

1 A bead slides on a fixed frictionless wire bent into a horizontal semicircle of radius R as shown in figure In addition to any normal forces exerted by the wire the bead is subjected to an external force that points directly away from origin and depends on distance r from the origin according to the formula F F R THE NAR b R A Given external force is a central force B Given external force is a conservation force 16F C Normal reaction by wire as bead leaves the wire is 3 D Speed of bead as it leaves the wire is A GROUP 16F R 3m

4 Read the given statements and select the correct option Statement 1 If a body is momentarily at rest it means that force and acceleration are necessa zero at that instant Statement 2 Force on a body at a given time is determined by the direction of motion only A Both statements 1 and 2 are true and statement 2 is the correct explanation of statement 1 B Both statements 1 and 2 are true but statement 2 is not the correct explanation of statement 1 C Statement 1 is true and statement 2 is false D Statement 1 is false and statement 2 is true

18 Three identical balls A B and C each of mass m connected by three identical springs when placed on a frictionless horizontal floor occupy corners of an equilateral triangle as shown in the figure This assembly is suspended by attaching the ball A to the ceiling with the help of a light thread What can you predict regarding accelerations of the balls immediately after the thread is cut Acceleration of free fall is g a All the balls will have downward acceleration g b All the balls have acceleration greater than g in different directions c Acceleration of the upper ball is 3g downwards and the accelerations of the lower balls are vanishingly small d Acceleration of the upper ball is 3g downwards and the lower balls move apart with finite accelerations 19 In the setup shown the pulleys the cords and the spring are ideal and masses of the loads are indicated in the figure Initially the system is in equilibrium What should be the range of mass M so that acceleration of 000mor greater than acceleration of free fall

3 A cylinder of mass M of radius R and of length L such that L 6R is hinged at point A in vertical position It suddenly starts to rotate about the hinge at A with an initial angular speed of wo Determine the support reactions at A in normal and tangential directions when the cylinder is in horizontal position 40 Points A Wo L 6R

A 50 kg person stands on a 25 kg platform He pulls a rope which is attached to the platform via the friction less pulley as shown in figure If the platform moves at a steady rate the force with which the person pulls the rope is Question Type Single Correct Type 1 2 3 500 N 250 N 25 N

Two identical masses A and B are on same vertical line A is released from rest while B is simultaneously projected upwards with a velocity of 50 m s Find the velocity of the combined mass just after collision considering perfectly inelastic collision g 10 m s A 1 20 m s 3 15 m s 50 m 50 m s B 2 5 m s 4 25 m sid A

point system is released from rest at that instant Bm O 1 AM acceleration to gravity Fig on th de th St 3 5g A Acceleration of point C is upward 2 B Acceleration of block B is 2g upwards C Acceleration of block A is g downward

of weight 20N and 100N respectively These are being pressed against a wall by a force F as shown If the coefficient of friction between the blocks is 0 1 and between block B and the wall is0 15 the frictional force applied by the wall on block B is EAE C

Q 6 A A particle of mass m is placed on the top of a smooth hemisphere of mass M The hemisphere is placed on force seen from the hemisphere frame acting on the particle as a function of angle 8 is given by smooth ground The particle is displaced gently Then ratio of magnitude of normal reaction and pseudo see figure Assume that the particle remains in contact with the hemisphere M m sin 0 B Msin 0 m M C M mcos 0 D M

A bead B of mass m 0 5 kg which can slide along a smooth horizontal rod is attached to one end of a light inextensible string of length 1 m as shown The other end A of the string is pulled with a constant speed vo 2 m s always directed along the length of the string Then choose the correct option s B 0 A

lustration 47 between them 30 N For the figure shown m frictional forces acting 10 kg m 15 kg and F 90 N Find the accelerations of the blocks an H 0 4 H4 0 2 A B F

In the figure shown all the surfaces are smooth The blocks A B and C have the same mass m F is floor and W is the wall Find the magnitude of the contact forces at all the surfaces after the system is released from rest The angle of inclination of the inclined plane with the horizontal is 0 B A C W

In the arrangement shown in figure m 1kg m 2kg Pulleys are masslesso al brouff ni and strings are light For what value of M the mass m moves with constant velocity Neglect friction brownw A 6 kg C 8 kg b browau Sp by B 4 kg sonol Isinoshod insbnsqeb smit D 10 kg nost M llug to or is no bensla a Hoold k

VO A block starts moving up an inclined plane of inclination 30 with an initial velocity of vo It comes back to its initial position with velocity 2 The value of the coefficient of kinetic friction between the block and the inclined plane is close The nearest integer to I is I to 1000 Answer

A loop of light inextensible string passes over smooth small pulleys A and B Two masses m and M are attached to the points O and C respectively Then the condition that m and M will cross each other Take AB 21 and AC AB nl will be A M n 1 Vn 3 2 1 B m M 2 n 3 n 1 1 C m M n 1 n 3 A ni WAM 1 D none of these MI B

ALLEN KLE offro in lo el 54 A force F 21 3k acts on a particle a F 0 5j 2k The torque acting on the partide relative to a point with co ordinates 2 0 m 0 3 0 m is 1 3 01 4 51 K N m 2 3i 6 k N m 3 201 4 0j k N m S

This section contains 10 questions Candidates have to attempt any 5 questions out of 10 If more than 5 questions are attempted then only first 5 attempted questions will be evaluated The answer to each question is a Numerical Value Type questions For each question enter the correct numerical value in decimal notation truncated rounded off to the second decimal place e g 6 25 7 00 0 33 30 30 27 127 30 if answer is 11 36777 then both 11 36 and 11 37 will be com Answer to each question will be evaluated according to the following marking scheme Full Marks 4 If ONLY the correct numerical value is entered as answer Zero Marks 0 In all other cases A spring scale indicates 10 N in the given situation as shown in fig Neglecting the mass of the pulley and ignoring friction between the cable and pulley the mass m in kg is g 10 ms wwwwwwww TIIT T

Consider a 2 kg block B connected to block A through a string passing over a pulley as shown in figure It is found that when the block A is 1 kg or more the block B slides on table when the car is stationary Now car starts moving with an acceleration on horizontal road It is seen that now the block B moves on the table when block A is 1 2 kg or more The acceleration of the car is a 3 m s c 2 m s B A b 1 m s d 4m s

Two blocks of masses 2 kg and 3 kg are tied at the ends of a light inextensible string passing over a frictionless pulley as shown 2 kg 2 36 N 3 48 N 4 18 N K 15 m s 3 kg If the system is accelerating upward with acceleration 5 m s the tension in the string is 1 24 N

A board of mass m is placed on a frictionless inclined plane that makes an angle 8 with the horizontal A block of mass M is placed on the board and is given a quick push up the board with initial velocity vo Find the distance d covered by the block by the time its velocity drops to vo 2 The board does not move relative to the plane 5v M 8g sin 0 M m 5v m 8g sin 0 M m 3v M 8g sin 0 M m 3v m 8g sin 0 M m 0

Wo blocks of mass 2 kg and 3 kg are placed in a cart A variable force F is acting on the Cart At an instant acceleration of different blocks and cart are as shown Find value of F at this instant mass of cart is 10 kg All accelerations are horizontal 2 kg a 3 kg af 21 A 27 N B 81 N C 30 N D 90 N Smooth 10 kg F 10 kg a 1m s a 3m s k 100N m 0000 2kg 2m s k 100N m 3kg 000 12 smooth 34 1

A smooth track is shown in figure A block of mass M is pushed against a spring of spring constant K fixed at the left end and is then released Find the initial compression of the spring so that the normal reaction at point P is zero oooo 3MgR K 2 MgR K 2 MgR K MgR M Circular part Radius R

4 None of the above A body of mass 10 kg is sliding on a frictionless surface with a velocity of 2ms The force require to keep it moving with a same velocity is 04036 S 1 10 N 2 5 N 3 2 5 N um 4 Zero A body of mass 2 kg is moving with a velocity 8 m s on a smooth surface If it is to be brought rest in 4 seconds then th

On stationary sail boat air is blown at the sails from a fan attached to the boat The boat wil 1 Remain stationary 2 Spin around 3 Move in a direction opposite to that in which air is blown 4 Move in the direction in which the air is blown

A rod slides on a fixed inclined plane and on a wedge which is moving horizontaly with an acceleration a towards right if the rod is always horizontal then magnitude of its acceleration is A a sin cosec a B a sina cosec a C a cos sec a D a cosa sec a BA a a

94 Two identical blocks are kept on a frictionless horizontal table and connected by a spring of stiffness k and of original length lo A total charge Q is distributed on the blocks such that maximum elongation of spring at equilibrium is equal to x Value of Qis a 210 4 ok lo x c 2 lo x 4 e okx b 2x 4 eok lo x d lo x 4 eokx

21 A body of mass m is moving in a straight line with momentum p Starting at time t 0 a force F at acts in the same direction on the moving particle during time interval of T So that its momentum changes from p to 2p The value of T is 2p a a b p www Va 10 C 2 2p a d 2p a

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 ao with which the Students B should climb up the rope to lift the Student A upward off the floor a 10 m s