Newton's law of motion Questions and Answers

2 At a given time the relative velocity of object A with respect to object B is 28j m s Assuming the top surface of both objects A and B remain horizontal a determine the velocity of each body at the instant depicted in the figure b Explain what does the result mean A L1Ix B 4 Starting from rest obje 50 The initial velocity of the distance travelled by t where v is the initial vele a Determine the distan b Draw the free body d

0 A small block of mass 3m is placed at height 5 2m on the curved surface of a wedge of mass 4m that can slide on the frictionless floor The curved incline ends parallel to the floor at the bottom and is frictionless The system is released from rest Find the speed of wedge 4m when the block reaches the floor Assume g 10m s and 3 1 732 Enter the answer in two decimal places h 4M 3m

A block of mass 100 kg is kept on a horizontal rough surface A man of mass 60 kg is trying to pull the block with the help of ideal inextensible string Find the minimum tension approximately in string to pull the block so that man remains at rest Coefficient of friction between block and horizontal surface is 0 2 and that between man and horizontal surface is 0 5 g 10 m s A 100 N C 180 N B 166 N D 196 N

9 In the frictionless pulley system shown all ropes and pulleys are massless and both blocks of masses M and 2M are at rest If block 2M is initially at h 15m from ground find its speed when it strikes the ground Assume 2 1 414 Enter the answer in two decimal places 2M

0 A spring block system is fixed in a train suddenly train starts moving with constant acceleration ao Taking origin at initial position of block what is equation of motion for block in reference frame of train Force constant of spring is k Neglect friction between block and train 1 2 mao k mmmmmmmm mao mao k k mao mao k COS COS mao COS k k m k t t t Aa Medical

4 A block of mass 2 kg is placed on a truck as shown in figure The coefficient of kinetic friction between the block and surface is 0 5 The truck starts from rest and moves with acceleration 8 m s After how much time the block fall off the truck 6m 1 4s 2 3s 3 2s 4 1 5 s 27

In the following figure triangular wedge is fixed All surfaces are smooth Pulley and string are ideal Fin tension in the string 8kg 30 1 4 g 4kg 2 2g 3 g 4 3g 32

The expression for downward acceleration of a body on an inclined plane of coefficient of friction and 0 inclination is 1 g sin 0 3 g sin 0 ucos 0 2 gsin 0 1 u 4 g sin 0 cos 0

57 A solid sphere of mass 1 kg radius 10 cm rolls down an inclined plane of height 7 m The velocity of its centre as it reaches the ground level is a 7 m s b 10 m s c 15 m s d 20 m s lle without slipping down an inclined

2 C Acceleration of the particle is constant D At t ls velocity of particle is 12 5 m s Three large boxes are kept stationary over one other as shown in figure A horizontal force 20 N acts on middle block as shown in figure Then M1 0 2 Sec Sr Super60 All H 0 8 My 0 3 1 Kg 1 Kg 1 Kg A Acceleration of lowest block is 4 5 m s B Acceleration of upper most block is 2m s C Friction between middle and lower block is 12N D Friction between middle and upper block is 2 N Space for rough work 20 N Page 3

Two blocks A and B of masses 3m and m respectively are connected by a massless and inextenisible string The whole system is suspended by a massless spring as shown in figure The magnitudes of acceleration of A and B immediately after the string is cut are respectively 3m 8m 9 1 9 3 2 1 31 9 3 9 9 4 19 12 9 1 20 32 3

PQ 33 In the given figure the tension in the string OB is 30 N Find the weight W and the tension in the string OA T a 30 3N 20 N c 30 3N 60 N T b 30 2N 80 N d 3 3N 10 N

Calcular el peso P necesario para mantener el equilibrio en el sistema mostrado en la figura En el cual A pesa 100 kg Q pesa 10 kg El plano y las poleas son lisas La cuerda AC es horizontal y la cuerda AB es paralela al plano 30 4 B P Calculate the weight P required to maintain equilibrium in the system shown in the figure In which A weighs 100 kg Q weighs 10 kg The plane and the pulleys are smooth The rope AC is horizontal and the rope AB is parallel to the plane

A circular wire frame of radius R is rotating about its fixed vertical diameter A bead on the wire remains at rest relative to the wire at a position in which the radius makes an angle with the vertical see figure There is no friction between the bead and the wire frame Prove that the bead will perform SHM in the reference frame of the wire if it is displaced a little from its equilibrium position Calculate the time period of oscillation 0 R

76 When 100 gram of liquid A at 100 C is added to 50 gram of a liquid B at 75 C the temperature of the mixture becomes 90 C The temperature of the mixture if 100 gram of liquid A at 100 C is added to 50 gram of liquid B at 50 C will be 1 70 C 2 85 C 380 C 4 60 C

0 10 A steel ball is floating in a trough of mercury If we fill the empty part of the trough with happen to the steel ball a It will continue in its position b It will move up c It will move down d It will oxecute vertical oscillations

In the figure a tin of anti oxidants m1 4 9 kg on a frictionless inclined surface is connected to a tin of corned beef m2 2 4 kg The pulley is massless and frictionless An upward force of magnitude F 5 6 N acts on the corned beef tin which has a downward acceleration of 4 9 m s2 What are the tension in the connecting cord and angle B

2 2 2 3 s 3 2 2 s 4 2 2 2 s see 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 1 2 2 s 9 49 pm

In the arrangement shown the pulleys are fixed 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 C 3 m A m m C m m m m S bood B m m 2m m g m m D 3 m

A particle of small mass m is joined to a very heavy body by a light string passing over a light pulley Both bodies are free to move The total downward force in the pulley is neglect m A mg C 4 mg B 2 mg D can not be determined

Figure shows a man of mass 50 kg standing on a light weighting machine kept in a box of mass 30 kg The box is hanging from a pulley fixed to theceiling throught a light rope the other end of which is held by the man himself If the man manages to keep the box at rest the weight shown by the machine is A 10 N B 100 N C 800 N D 200 N K

Question 30 A body starts from rest and travels with uniform acceleration on a straight line If itsvelocity after making a displacement of 32 m is 8 m s its acceleration is a 1 m s b 2 m s c 3 m s

Question 16 A particle of mass 0 3 kg is subjected to a force F kx with k 15 N m What will be itsinitial acceleration if it is released from a point 20 cm away from the origin W a 15 m s b 3 m s c 10 m s d 5 m s

10 Four forces act on a point object The object will be in equilibrium if vector sum of all forces be zero they are opposite to each other in pairs the sum of x y and z components of forces is zero separately All of these

Question 19 The frame of reference attached to a satellite of the earth is a an inertial frame b an absolute frame at rest with respect to the stars c a non inertial frame d a gravitational frame

des and the ratio s fly off each to 144 2 particle t while 28 A and B are of mass m and C is of mass M If the system is in equilibrium then J anitude al to CAMERA that Goudsep Horn Anka A m M 2m M 2m 3 M 2m 4 M m 0 D C M M B m img rimg 2m Cel 2021 2T COSO mg cost 3 32 The maximum height at which a small can be placed on the parabolic bowl slipping is 0 5 Equation of parabolic bowl is s Where x and y are in metre y m 2021 08 11 14 24

is Set 20 1 97 10 kg 40 kg ily balance in the system shown wwww www 20 kg 2 60 kg F nha V LT an a 2a 3 a 4a 35 A coin placed it is placed at the angular ve will just slip a 1 3 cm 3 2 cm ums mut b 20 3 kg 4 40 kg 3 32 The maximum height at which a small mass m

H3 Billy is perched on the end of a diving board Find the normal forces of the supports on the diving board Note one of these forces will be directed downward billy mig 820 N board mag

2 a A freighter is 240 km due east of a harbor A current is flowing due south and the freighter captain wishes to set a course so that he can reach the harbor directly He sets the course at 22 6 north of west and sets a speed through the water of 13 kmh and the freighter eventually reaches the harbor in 20 hours Determine the velocity of the current 3 mark b Vector A has a magnitude of 8 00 units and makes an angle of 45 0 with the positive x axis Vector B also has a magnitude of 8 00 units and is directed along the negative x axis Find i the vector sum A B ii the vector difference A B c A 2 kilogram block initially hangs at rest at the end of two 1 meter strings of negligible mass as shown on the left diagram below A 0 003 kg bullet moving horizontally with a speed of 1000 meters per second strikes the block and becomes embedded in it After the collision the bullet block combination swings upward but does not rotate Please refer to Figure 2 1 1000 m s 0 003 kg 2 kg Before Collision 3 mark 3 mark 1 m Immediately After Collision Figure 2 1 i Calculate the speed v of the bullet block combination just after the collision 3 mark ii Calculate the ratio of the initial kinetic energy of the bullet to the kinetic energy of the bullet block combination immediately after the collision 4 mark iii Calculate the maximum vertical height above the initial rest position reached by the bullet block combination 4 mark

1 The motorized drum turns clockwise at constant speed causing the vertical cable to have a constant downward velocity v As part of the design of the system determine the tension Tin the cable in terms of the y coordinate of the cylinder of mass m Neglect the diameter and mass of the small pulleys Figure 3 48 Ref 3 48 Dynamics JL Meriam 6th Edition C 0 mg fo

m of ring iv In figure shown if 2 kg block is moving at an acceleration 2 m s find the elongation in spring and acceleration of 4 kg block at this instant Take g 10 m s 0 012 m 2 m s 4 kg 0 1 k 1000 N m 6oooooooooo Figure 2 120 2 kg 0 2 20 N

A solid cone of mass m 1 kg is placed on a plank of mass M 1 kg which is placed on a smooth horizontal plane The coefficient of friction between cone and plank is If horizontal force F is applied on the plank for which cone is in equilibrium with respect to plank given g 10 m s 2 then 20 A Answer A B C D Your Attempt Correct answer Maximum force applied on plank is 5 N Maximum force on the plank is 4 N Friction force on the plank is 2 N Friction force on the plank is 2 5 N Rate this ques

Q 39 A rocket is fired upwards It emits gases at a speed of 10 km s w r t rock et 5kg of fuel is burnt per second in the rocket Find the upthrust force acting o n the rocket Also calculate the velocity of rocket at t 0s t 10s Initial mass of rocket is 2000kg Assu me gravity free space ANswer is FOOO

lock on the sphere shown in figure is in equilibrium it implies that net force is zero If sphere applies a force N of 3 N on the block in the direction erpendicular to the surface of the sphere and weight of the block mg is 5 N vertically downward Find the force applied by the string on the block T if it a angentially Assuming sphere is fixed smooth J mg

An object of mass 25 kg moves along a straight line on a smooth horizontal surface A force F acts on the object in its direction 20 of motion The graph of the force against time is shown here What is the velocity of the object at t 8 s if its velocity at t 5 s is 4 m s A 3 5 m sl B F N 0 4 4 9 m s 8 1 E

In the figure acceleration of blocks A B and C are indicated by a b and c respectively Acceleration a b and c are w r t to the ground Find the acceleration of the block A in terms of b and c if the surface is smooth and pulley and string are ideal be A B

A wedge of mass M and two springs of spring constants K and K are kept on a smooth horizontal plane and both the springs are in natural lengths Ther sphere of mass M is put slowly as shown in given figure When sphere is at rest on the wedge then K 2 K and K K Expansion in spring with spring constant K is Mg 3K Compression in spring with spring constant K is 2Mg 3K A M K 60 M K Expansion in spring with spring constant K is equal to the compression in spring with spring constant K Expansion in spring with spring constant K is 50 of compression in spring with spring constant K

All except one of the following require the application of a net force Which one is the exception Changing an object from a state of rest to a state of motion Changing an object s speed without changing its direction of motion Maintaining an object in motion at a constant velocity Maintaining an object in uniform circular motion Changing an object s direction of motion without changing its speed

The frictional force due to air resistance acting on an object is always greater than the net force in the direction of the object s motion in the opposite direction to the object s motion in the upward direction smaller than object s weight

A body of mass 10 kg lies on a rough inclined 3 plane of inclination sin 5 1 OA L 2 OB horizontal When a force of 30N is applied on the block parallel to and upward the plane the total reaction by the plane on the block is nearly along BON B ALLEN D 00 3 OC with the 4 OD 30 10 kg af van safe and quat an a fer fagfart 30N 1 OA 2 OB 3 OC sin 5 a occh fan f 4 OD

4 25 N If the blocks are placed on smooth plane shown in figure If they simultaneously on smooth plane then find force exerted R by 20 kg block on 5 kg block R 1 15 N 3 Zero Course I II 20 kg 10 kg 5 kg 0 30 2 35 N 4 None ram are released ne questionpas 35 20 N 4 25 N a Equi T HOE v B si t ch UTRA B I a 20 kg 35 kg faust after a Huche 1 15 N 3 Zero Re 20 kg 10 kg 5 kg 0 30 2 4 35

Two blocks of mass M 6 kg and m 3 kg are placed 32 as shown in the figure Coefficient of friction between M and m is 0 5 Coefficient of friction between M and the surface is 0 4 The maximum horizontal force that can be applied to the mass M so that they move without separation is g 10 ms m 3 kg M 6 kg 1 41 N 3 81 N Course 1 11 01 42 2 61 N 4 101 N legs M 6 f m 3 fanu at gant an faeigen 0 51 M 1 41 N 3 81 N 0 41 fan My FREI After T g 10 ms2 m 3 kg M 6 kg 2 61 N 4 101 N 1001CMD300120008 E H 19092020

The sum of magnitudes perpendicular to smaller A 6N and 10N of two forces acting at a point is 16N If the resultant force is 8N and its direction is force then the forces are es B SN and Near C 4N and 12N T 8N 8N D 2N and 14N

rad Example 2 2 A man wishes to estimate the distance of a nearby tower from him He stands at a point A AC upto B a distance of 100 m and sees O again Since O is very distant the direction BO is practically in front of the tower C and spots a very distant object O in line with AC He then walks perpendicular to the same as AO but he finds the line of sight of C shifted from the original line of sight by an angle e 40

13 If a current carrying circular loop is placed in non uniform magnetic field then 1 Force and torque must be non zero 2 Force and torque must be zero 3 Force must be non zero but torque may be zero A Forgo and torque moy ho toro

suppose a stone is moving linearly under no external force not even gravity and it hits a mirror and breaks it down Then what factor was responsible for the breaking down of that mirror Was it the Kinetic energy of the stone Or is it momentum edited 12 47 PM

A block of mass 2 kg is pulled along a horizontal surface by applying a force at an angle 30 with the horizontal If the block travels with a uniform velocity and has a displacement 115 cm and the coefficient of friction is 0 15 then the work done by the applied force is

17 Two blocks A and B each of mass m are connected by an ideal string that passes over two fixed ideal pulleys The blocks are also connected with the ground by springs of force constants k and k k k When both the springs are relaxed the block A is pulled down a distance x and released Acceleration magnitudes of the blocks A and B immediately after the release are a and a respectively Mark the correct options a c a az if k k 2mg x b a d a a a if k k 2mglx

5 35 A block of mass m 2 kg slides along a frictionless table with a speed of 10 m s Directly infront of it and moving in the same direction is a block of mass m 5 kg moving at 3 m s A massless spring with a spring constant 11 2 N cm is attached to me as shown in figure 5 146 When the block collide what is the maximum compression of the spring Assume that the spring does not bend m k frrrrrrrrrrrro m

ABCD is a wire frame of identical wires in which point D is given velocity v as shown in figure Choose the correct statement s O 0 A 30 D Velocity of point A along x axis will be v 2 Speed of point A will be v Speed of point A along y axis will be v 2 Velocity of point A will be equal to velocity of point C