Newton's law of motion Questions and Answers

3 In the given diagram if the spring connecting D and C is cut then what will be the accelerations of blocks A B C D at that instant A 0 g g 1 0 4g 0 1 1 1 C 0 Bee 4kg elle 3kg B2kg 1kg B 0 1 1 3 D g 1 3 g 1 5

S 15 Three identical cylinders each of mass m 10 3 kg are arranged on a horizontal floor as shown in the figure with their axes horizontal The floor as well as the cylinders are frictionless You apply a constant horizontal force directed to the right on the left cylinder For what range of F will all three cylinders remain in contact with each other Acceleration of free fall is g 10 m s

A 59 0 kg ice skater is moving at 3 98 m s when she grabs the loose end of a rope the opposite end of which is tied to a pole She then moves in a circle of radius 0 850 m around t pole a Determine the magnitude of the force exerted by the horizontal rope on her arms KN b Compare this force with her weight

kg and m2 2 0 kg are connected by a at rest on a smooth horizontal surface with the spring at its natural length F m ooooooo m A horizontal force of constant magnitude F 6 0 N is applied to the block my for a certain time t in which mi suffers a displacement Ax 0 1 m and Ax2 0 05 m Kinetic energy of the system with respect to center of mass is 0 1 J The force F is then withdrawn a Calculate t b Calculate the speed and the kinetic energy of the center of mass after the force is withdrawn c Calculate the energy stored in the system

A particle moves in the xy plane under the action of a force F such that the value of its linear momentum P at any time t is P 2 cost P 2 sint The angle between P and F at that time t will be X y B 30 D 180 A 0 Jej 90

3 A pulley is attached to the ceiling at point B by a cable of length 8 m See the diagram A rope of length 54m is attached to the wall at point A 5 m from the ceiling and then runs through a movable pulley on a track along the ceiling The wall is 20 m from point B The rope passes through the two pulleys and is connected to a weight When the weight is released it comes to rests at a point W that maximizes the distance d between the weight and the ceiling The top pulley ends up a position x m from the wall 5m Tope 20 m trope W 8 m Find the location of the pulley and point C i e x and y which result in a maximum distance d Quote your answer as three numbers x y and d

1 A block of mass m is placed on a smooth inclined plane of inclination of 6 with the horizontal The force exerted by the plane on the block has a magnitude A mg C mg cost B mg cos0 D mg tane

Lo B 51 In the setup shown a small block A of mass m suspended from a peg with the help of a light inextensible cord rests on a vertical face of a block B of mass M which is held motionless on the horizontal ground Inclination of the cord with the vertical is and all the surfaces in contact are frictionless Find acceleration of the block B immediately after it is released Acceleration due to gravity is g

A stone of mass 1 kg tied to a light inextensible string of 10 length L 3 m is whirling in a circular path of radius Lin a vertical plane If the ratio of the maximum tension in the string to the minimum tension in the string is 4 and if g is taken to be 10m sec the speed of the stone at the highes point of the circle is CBSE PMT 1990 a 20m sec c 5 2 m sec b 10 3m sec d 10m sec

9 Three blocks of masses m m and m are connected as shown in the figure 5 W10 All the surfaces are frictionless and the string and the pulleys are light Find the acceleration of m m 0 M A B M3

7 A light inextensible rope is hanging vertically passing over a pulley Two monkeys M M of equal weights hang from the opposite ends of the rope such that both at same level Now one of the monkeys say M starts climbing up the rope Select the correct choice 1 M will reach up to the pulley first 2 M will never be able to reach upto the pulley 3 Both M and M will reach the pulley at same time 4 M will reach the pulley first

Two blocks of masses mi 1kg and m2 2kg are connected by a spring of constant k 100 N m and placed over a plank as shown The coefficient of friction between me and plank is 0 5 and there is no friction between m and plank Initially the whole sys 2m s2 Find the maximum compression of the spring i is at rest The plank is now pulled to right with constant acceleration a k www m m a 2m s

In the situation as shown in figure if acceleration of B is a vertically downwards then find the acceleration of A Wedge A is free to move M B C a sin 0 a cote 2a tan 0

0 Gravel is dropped onto a conveyer belt at a rate 40 of 0 5 kg s The extra force required in newton to keep the belt moving at 2 m s is 1 IN 2 2N 3 4 N 4 0 5 N 0 5 kg s 2m s STERKER EEN HA PR 1 IN 2 2N 3 4 N A FORE fe 4 0 5 N

Two bars of masses m and m connected by a non deformed light spring rest on a horizontal plane The coefficient of friction between the bars and the surface is equal to u What minimum constant force has to be applied in the horizontal direction to the bar of mass m in order to shift the other bar m

Three forces acting on a body are shown in the figure Ta have the resultant force only along the y direction the magnitude of the minimum additional force needed is CBSE PMT 2008 IN a 3 N b 3N c 0 5N d 1 5 N 4N y 30 60 2N

A non conducting uniform rod of mass 1 kg and length 1 m is hinged at one end as shown in the figure A charge q 1 C is uniformly distributed over its length The rod is released from rest in a uniform magnetic field of 2v15T at time t 0 from the position shown Find the hinge reaction in Newton when the rod becomes vertical Take g 10 m s X X X X XX X X X X X X X X X X O X X X 60 XXX X X X X X X X X L X X X X X X X X XL t 0 X X X X XX X X X X X X X x X X X X X X X X X X X X X X X X

PROBLEM 3 3 A crate whose mass m is 360 kg rests on the bed of a truck that is moving at a speed vo of 105 km h The driver applies the brakes and slows to a speed v of 62 km h in 17 s What force assumed constant acts on the crate during this time Assume that the crate does not slide on the truck bed Solution We first find the constant acceleration of the crate Solving Eq 2 26 Vx Vox axt for a yields km h km h s h s ax Vx Vox t V V x a t X Ox Convert velocity in km h to velocity in m s by multiplying V by 10 3600 m s In the above equation substitute Vx 62 km h Vo 105km h and t 17 sec and calculate a The force FCT exerted on the crate by the truck follows from Newton s second law FCT max kg m s Substitute for m 360 kg and a and calculate as above m s N

Topic The mass of a body measured by a physical 1 balance in a lift at rest is found to be m If the lift is going up with an acceleration a its mass will be measured as 1 m 1 m 2 m 4 Zero PIT za gela af f 1 m 1 3 m 2 m 4 a 4 COLU

Three identical masses are at the three corners of the triangle connected by massless identical springs rest length o forming an isosceles right angle triangle If the two sides of equal length of length 200 lie along positive x axis and positive y axis then the force on the mass that is not at the origin but on the x axis is given by ax by with O a 2 and b 1 O a 1 and b 0 a 2 and b 1 O a 0 and b 1 2 andh a

A lift is moving vertically upward with an acceleration a The acceleration of a body dropped freely by a man moving with lift with respect to ground is 1 g a 3 g 2 g a 4 Zero

A particle of mass m is made to move with uniform speed along the perimeter of a regular polygon of 2 n side The magnitude of impulse applied at each corner of the polygon is Options 1 2mu sin 2 m U sin T 2n 3 mu cos 75 2n 7 2n

28 A light rigid pipe is suspended with the help of two light in vertical threads Inside the pipe two balls one of mass m an mass 2m can slide without friction Initially the pipe is horiz the balls stay equidistant from each other and from the ends as shown in the figure How many times will the tension for thread A change immediately after the thread B is cut

21 The graph of force versus displacement is shown 25 For head on collision betw equal radii r the impact in figure A body of mass 2 kg has a velocity of 20 m s at x 0 Find the kinetic energy of body at x 12r 10 m F N 10 N 12 N 436 436 J 3 484 J C 4 A D 10 Cree 2021 X m 2 460 J 4 282 J 26 126 3 More than 2r A car of mass m is mo radius r with a speed wh tas v kt where k is power delivered by ag 1 mkt 3 mk t 127 A force F k yi

The force of repulsion between two point charges is F when these are 1 m apart Now the point charges are replaced by conducting spheres of radii 5 cm having the charge same as that of point charges The distance between their centres is 1 m then the force of replusion will 1 increase 2 decrease LOL 10F

In the arrangement shown in the figure initially the block of mass m is in limiting equilibrium The coefficient of friction between the block of mass m and floor is Now the particle of mass m is given a horizontal velocity v The initial distance of the block of mass m from the pulley is The masses of pulley and threads are negligible Choose the correct option s m A Acceleration of m just after the velocity given is m 1 l v 20 B Acceleration of m just after the velocity given is C Radius of curvature of path of m just after the velocity given is 1 D Radius of curvature of path of m just after the velocity given is 2 1 1 1

A glass marble whose mass is 10 kg falls from a height of 2 5 m and rebounds to a height of 1 6 m If the time during which they are in contact be one tenth of a second then the average force between the marble and floor is 112 6 N 3 17 2 N M FAT 182 506 2 17 N 4 18 4 N

A cylinder of mass m rests in a supporting block as shown If 60 and 0 30 calculate the maximum acceleration at which the block may be given up the incline so that the cylinder does not lose contact at B neglect friction anywhere A g 2 B g B 8 B C 2g D g 4

In the figure a man of mass 60 kg is standing inside a box with the help of a rope as shown on the weighing machine fixed to the box The weight of box along with weighing machine is 30 kg The reading of spring balance is S and reading of weighing machine is B Q If the reading of weighing machine is equal to weight of man the reading of spring balance is kg wt A 180 HMMMM O B 60

3M 4m In the figure shown the relation between the accelerations of A B C is here a relative to C 5 1 a b c 0 2 a b c Sm 3 a b c 4 None of these 24 aptal in figura m 1ke and m B C acceleration of A 124 Aapo 84 93 9 20 2kg while all the pulleys and strings are 8 1 3 The

container of mass 20 Kg is moving towards right by applying a constant horizontal force 100 N Initial velocity of container is zero and is falling in container with a constant rate of 1kg sec with the help of fixed cone as shown in the figure Find the velocity of the container in m s at t 100 sec

2 Two particles are connected by a light string of length 2Ra The system is draped ove of radius R as shown in the figure coefficient of static friction being 3 The angle 0 in degrees when the system is in equilibrium and about to slide is 0 the value of 00 10 10 2o cic ech mu q g in FORTI fa fal Ral 34 faalger tal 4 an any fud all f a 0

In the system shown in the figure the block A can slide smoothly between the inclined surface of the wedge and the vertical wall The wedge B is moving at 2 m s towards left What will be the speed in m s of the block A B A 37

3 Three concurrent co planar forces 1 N 2 N and 3 N acting along different directions on a body a can keep the body in equilibrium if2 N and 3 N act at right angle b can keep the body in equilibrium if 1 N and 2 N act at right angle c cannot keep the body in equilibrium d can keep the body in equilibrium if 1 N and 3 N act at an acute angle

5 A passenger getting down from a moving bus falls in the direction of the motion of the bus This is an example for a inertia of motion c third law of motion d inertia of rest b second law of motion

In shown figure pulleys and strings are ideal and horizontal surface is smooth The block C of mass 2m is given a horizontal velocity of vo 3 m s towards right and the rest of the system is released from rest at same instant MA 2m M m g 10 m s2 Choose the correct Statement s Vo The velocity of mass C just after the string regain tension is m s The velocity of mass B just after the strings regain tension is 38 m s The velocity of mass A just after the strings regain tension is m s 36 The momentum of center of mass of all three blocks is not constant A2m m B

A truck moves a distance of 50 km It covers first half of the distance at speed of 200 m s and second half at speed v If average speed of truck is 100 m s then value of vis 1 200 m s 3 100 m s 3 2 200 3 m s 4 100 m s

arranged as shown S is a spring balance An additional force F is applied to m to keep the system at rest then g 10 m s Assume spring balance gives in reading in Newton m W S m A the reading in the spring balance is 110 N B the reading in the spring balance is 70 N C F the reading in the spring balance D F the reading in the spring balance Answer B C Solution Conceptual

kg homogenous bar AB rests on two frictionless ramps with different angles of inclination shown If a solid block of mass M 30 kg is placed on the bar determine the distance x so that the bar remains horizontal A 60 X 10m 40 M B

For the system shown in figure the force exerted by the axis on the pulley is 20 kg a 20 b 40 N at an angle 45 with the horizontal not an angle 45 with the horizontal d 5 kg 80 40 2 N at an angle 60 with the horiz 40 N at an angle 60 with the horizont inclined plane with

A block is placed an inclined plane moving towards right with an acceleration a g The length of the inclined plane is o All the surfaces are smooth Find the time taken by the block to reach from bottom to top of the inclined plane angle of inclined plane is 30 with horizontal 20 1 8 3 1 Co 2 3 1 400 3 3 1 20 4 38

A 30 kg block is kept over a 60 kg block as shown in figure Horizontal force F is applied on the lower block and it is found that upper block moves with acceleration 2 m s and lower block moves with acceleration 5 m s2 There is friction between the blocks but surface below 60 kg block is smooth A 30kg B 60kg TT 1 Force of friction between the blocks is 2 Applied force F 450 N 3 Net force on block B is 300 N 4 Net force on block A is 90 N 90 N F

0 A boy fallen freely from a building of height 320 m After 5 second superman jumps downward with initial speed u Such that the boy can be saved The minimum value of u is assume g 10 m s 1 95 1 m s 2 98 3 m s 3 91 6 m s 4 856 m

The string between blocks of mass 2m and 3m is massless and inextensible The system is suspended by a massless spring as shown If the string is cut find the magnitudes of accelerations of mass 3m and 2m immediately after cutting 1 8 2 8 3 28 8 13m 2m

A ball is dropped from the roof of a lift At this moment the lift is moving downward with an acceleration a a g The ratio of acceleration of the ball for an observer inside the lift to the acceleration of ball for an observer on the ground will be 1 g a g 3 g a g 2 g g a 4 g a g a

Two blocks of mass 2 kg and M 5 kg are in contact on a frictionless table A horizonatal force F 35 N is applies to m Find the force of contact between the block will the force of contact remain same if F is applied to M F m M

A man weighs 80 kg He stands on a weighing scale in the lift which is moving upwards with a uniform acceleration of 8 m s What would be the reading on the scale g 10m s 1 Zero 2 1400 N 3 1440 N 4 1480 N

Request two children to stand on two separate carts as shown in Fig 9 13 Give them a bag full of sand or some other heavy object Ask them to play a game of catch with the bag Does each of them experience an instantaneous force as a result of throwing the sand bag You can paint a white line on cartwheels to observe the motion of the two carts when the children throw the bag towards each other

The system shown is in equilibrium Find the acceleration of the blocks A B C all of equal masses m at the instant when Assume springs to be ideal i the spring between ceiling A is cut ii The string inextensible between A B is cut iii The spring between B C is cut Also find the tension in the string when the system is at rest and in the above 3 cases eeeeeee mmm k

Brooke almost got caught the last time she took Mayra s box of red vines But when Mayra gets a new 276 pound box of red vines 125 kg for her birthday Brooke can t resist As the party winds down and people begin to leave Brooke waits until Mayra goes to the bathroom before making her move But with a box this big Brooke decides to pull it instead She ties the ribbons from Mayra s birthday presents together wraps it around the box of red vines and pulls with a force of 750 N at an angle of 25 degrees above the horizontal If the coefficient of friction between the box and the carpet is 0 7 what is the acceleration of Mayra s box of red vines 2 2 m s 2 7 3 m s 2 4 6 m s 2 0 35 m s 2