Newton's law of motion Questions and Answers

Block A of mass mA 200 g is placed on an incline plane and a constant force F 2 2 N is applied on it parallel to the incline Taking the initial position of the block as origin and up along the incline as x direction the position x time t graph of the block is recorded see figure b The same experiment is repeated with another block B of mass mg 500 g Same force F is applied to it up along the incline and its position time graph is recorded see figure b Now the two blocks are connected by a light string and released on the same incline as shown in figure c Find the tension in the string x m X 0 2 0 0 5 O 0 5 1 0 2 0 t sec B

for ex v u at as we know that a dv dt adt dv Integrating both sides so Integration of adt is at because of constar acceleration

A block is kept on a frictionless inclined surface with angle of inclination a The incline is given an acceleration a to keep the block stationary Then a is equal to 1 g 2 g tan a 3 g tan a 4 g cosec a

A plate bent at right angles along its centre line is placed onto a horizontal fixed cylinder of radius R as shown The minimum co efficient of friction between the cylinder and the plate so that plate does not slip The value of x off the cylinder will be 4x 2 1 is B

A particles starts from point A with constant speed v on a circle of radius R Find magnitude of average velocity during its journey from C a A to B b A to C c A to D D Of B

A belt is moving against a fixed cylindrical drum of radius R with a very small constant speed as shown in figure top view of the arrangement The segment of the belt in contact with drum makes an angle of at centre axis of cylindrical drum If u is the coefficient of friction between belt cylinder then correct relation between tension in belt at A T B T is A T Te B T Tes A C T TA XH D T T x A R B Direction of motion of belt

You hit a tennis ball against a wall Explain any and all incorrect ideas in the following description of the physics involved According to Newton s third law there has to be a force opposite to your force on the ball The opposite force is the ball s mass which resists acceleration and also air resistance

Two cars P and Q start from a point at the same time in a straight line and their positions are represented by Xp t at bt and X t ft t At what time do the cars have the same velocity A B C D 1 b a4f 2 b 1 2 1 b 2 146

known as impulse represente Fxt 9 Long answers plain Newton s third law of motion with two examples stion

Two blocks A and B are connected by a light string The mass of A is m and of B is M The wedge is fixed and pulley is massless Th system can t be at rest if M is greater than Pm or M is less than Qm where P and Q are positive numbers Find value of PxQ A m 45 smooth rough M A 0 5 45

4 15 min with a A particle starts from origin at t 0 s velocity 4 0 m s and moves in x y plane with a constant acceleration of 6i 41 m s The time after which y coordinate of particle will be 48 m will be NCERT Pg 87 1 6 s 2 4 s 3 8 s C

A block P of mass 4 kg is placed on horizontal rough surface with coefficient of friction 0 6 And two blocks R and Q of masses 2 kg and 4 kg connected with the help of massless strings A and B respectively passing over frictionless pulleys as shown then g 10m s P A 4kg 4kg 2 A acceleration of block P is zero C tension in string B is 40 N Which of the following stat B 0 6 2kg R B tension in string A is 20 N D contact force on block P by table is 20 5 N

5 If pulling force P is applied at angle 0 with the vertical on a block of mass m as shown in the given diagram then the force applied by the block on the floor is 1 mg 3 mg P sine m P 2 mg P sine 4 mg P cose

on a horizontal smooth table A block of mass m is placed at the mid point of the smooth inclined surface having length L along its line of greatest slope Inclination of the inclined surface is 0 45 The block is released and simultaneously a constant horizontal force F is applied on the wedge as shown a What is value of F if the block does not slide on the wedge b In how much time the block will come out of the incline surface if applied force is 1 5 times that found in part a L m

SINGLE ANSWER CORRECT TYPE A block comes down a stationary inclined plane of angle of inclination with a constar velocity The acceleration with which the incline should be moved towards right horizontally so that the block now moves upwards with constant velocity is A g sin 20 B g cos 20 C g tan 20 D g cot 20 0 a

Three identical balls are connected through massless inextensible strings The string connecting A and E passes through a hole in a frictionless horizontal table A is performing uniform circular motion while B and C are stationary Just after cutting the string between B and C A B Acceleration of c is g down ward Acceleration of B is g 2 upward Acceleration of A is 3g 2 radially inward DTension in string between A and B reduces by 25 A C

A uniform red of length 12 metre and mass m is hinged at midpoint and lies horizontally at rest Rod is free to rotate in vertical plane about hinge O A particle of mass m is released from height h as shown in figure Particle collides with end A and sticks to it Calculate minimum height h in metre so that system can complete vertical circular motion

A 324 lb weight is being help up by a block and tackle pulley system of 3 attached pulleys also attached to the weight and three attached pulleys hooked to the ceiling If a rope is tied to a hook on the bottom set of pulleys then strung through a 1st top pulley then 1st bottom pulley then 2nd top pulley 2nd bottom pulley 3rd top pulley 3rd bottom pulley then rope held up by a person What is the tension in the rope

9 One end of massless rope which passes over a massless and frictionless pulley P is tied to a hook C The other end is free Maximum tension that the rope can bear is 640 N With what value of maximum acceleration in ms 2 can a man of 40 kg climb up the rope Take g 10 ms 1 16 2 12 3 8 U

44 A body of mass 2 kg is kept stationary by pressing to a vertical wall by a force of 100 N The coefficient of friction between wall and body is 0 3 Then the frictional force is equal to g 10 m s 1 6 N 2 20 N 3 600 N 4 700 N

A body A weighing W descends down on an inclined plane D which makes an angle a with the horizontal and pulls a load B that weighs W by means of a weightless and inextensible thread passing over a small light pulley C as shown in figure If the horizontal component of 20K in newton with which the the force is 75 inclined plane D applied on the floor corner E Find the value of K Take a 37 W 40 N W 20 N neglect friction C B E D a A

You are on a frictionless horizontal plane How can you move horizontally if no horizontal force is exerted by pushing against the surface By rolling your body on surface By running on surface By spitting or sneezing

ector B has x y and z components of 1 00 3 00 and 4 00 units respectively Calculate the magnitude of B and the angles that B makes with the coordinate axes 8 79 53 38 8 11 30 38 26 79 53 38 26 11 30 38

the wedge The system is released from rest az is absolute acceleration of the block and a is absolute acceleration of the wedge The string is inextensible Then 1 2 a 2 45 1 a 3 i 2 1 3 a2 2 1 1 L

A student wants to determine the coefficients of static friction and kinetic friction between a box and a plank He places the box on the plank and gradually raises the plank When the angle of inclination with the horizontal reaches 30 the block starts to slip and slides 4 0 m down s 10 the plank in 4 0 s If is given by then B find the value of u u are coefficient of static friction kinetic friction

If both masses are at rest then choose incorrect option M m A Tension in string is mg B Tension in string is Mg if Mm C Tension in string is Mg if M m D Masses can move if m M

An athelete runs up and projects Javelin at a certain angle to the horizontal If the speed of the Javelin relative to the athelete is equal to the speed of the athelete at the time of projection what should be the angle at which he should throw relative to himself so that the range is maximum The height of the athelete can be considered negligible A 45 B 30 C 60 D 37

A beaker of radius r is filled with water refractive index up to a height H as shown in the fi on the left The beaker is kept on a horizontal table rotating with angular speed w This makes water surface curved so that the difference in the height of water level at the center and at circumference of the beaker is h h H h r as shown in the figure on the right Take surface to be approximately spherical with a radius of curvature R Which of the following is correct g is the acceleration due to gravity A R B R h r 2h 3r 2h H A 3H C Apparent depth of the bottom of the beaker is close to 3 1 H D Apparent depth of the bottom of the beaker is close to 3 1 H 4g h

At an airport terminal a passenger A uses the walkway and carries his heavy luggage along with him Passenger B walks alongside the way while the passenger C walks on it both B and C walking briskly at 1 2 m s The walkway is 40 m long and moves at 0 80 ms Calculate how long does it take for A B and C to reach the other of the walkway Ans A 50 s B 33 s C 20 s

A uniform rope of length L and mass M is placed on a smooth fixed wedge as shown Both ends of rope are at same horizontal level The rope is initially released from rest then the magnitude of initial acceleration of rope is A Zero C tan atan B g B B cos acos B g D None of these

A particle is situated at the origin of a coordinate system The following four forces begin to act on the particle simultaneously F 2 3 k N F 31 j k N F3 2 5 3k N F4 5i 31 3k N The particle will move A along x axis B along y axis C in x y plane but not along x or y axis D in y z plane

In the setup shown the pulley and the threads are ideal the spring of force constant k is massless the wheel has all its mass m uniformly distributed in its rim the harness used to connect wheel axle with the spring and with the thread is massless and the loads A and B are of masses m and 3m respectively Initially the harness is held motionless keeping the spring relaxed and then released If the wheel rolls on the horizontal tabletop without slipping find maximum tension developed in the thread connecting the loads 0000000 A B

SECTION II Answer any THREE from the FIVE assume g 10 m s If required V m s Question ONE Kinematics 5 5 1 The graph shows a car starts moving first with uniform acceleration of 5 m s for 8s then uniformly for some time and finally decelerates at 8 m s and comes to a stop The total journey is for 24s a Find the maximum velocity X reached b c X 3 x 10 30 Find the average speed for the whole journey Find t and hence find how long the car travelled at that constant speed X Distance m

A block of mass 2 2 kg is accelerated across a rough surface with the help of a string as shown Tension is the string is maintained at 10N and the pulley is 0 1 m above the top of the block g 9 8 ms Wa When x is large acceleration of block is approximately 0 625 m s Maximum value of acceleration is approximately 0 976 m s For x 6 10 cm acceleration of block is nearly zero Acceleration of block will never be zero m X Tho u 04

Three blocks A B and C of masses 8kg 4kg and 1kg respectively are in contact on a frictionless surface as shown If a force of 26N is applied on the 8kg block then the contact force between A and B is a 8 N b 18N C 1N d 10N A B 20

The net force in newtons acting on a body of mass 2kg at rest varies with time t in microseconds as shown in the figure AB BC and CD are straight line segments Find velocity of the block at 16 s 800 O 29 x 103 m s 29 10 m s O 5 x 10 m s None of these Force F 600 400 200 2 B D 6 8 10 12 14 16 Time us 4

A cricket ball of mass m is thrown at a certain speed u in a direction 0 above the horizontal During the entire journey the force acting on the ball is 1 1 22 1 mg sine 2 mg cose 3 mg 4 Zero

A small body is projected vertically upwards with speed u in a medium where a resistance force proportional to square of it s speed acts on it body in this medium is found to be equal to vo Maximum height attained by the body will be u v O en 2g u 2v2 21 mm 1 V en resistance mkv where m is the mass of body Terminal speed

A canon fires down a 45 slope as shown At what angle e above the horizontal should the cannon fire in order to maximize the time the cannon ball spends in the air Neglect air resistance 3 A 45 B 90 C 22 5 D 37 5 45

A car starts from origin towards positive x axis with a constant speed of 10m s It takes left turns after 2 sec 4 sec and 6 sec It always moves in a straight line except while turning Displacement of the car after 5 sec will be A 50 meter B 10 5 me meter C 10 17 metre D 40 2 me metre

Two bodies of masses 8 kg and 12 kg are on a horizontal surface and are connected by a string The 8 kg body is pulled with a force 59 N If the coefficient of friction for all the surfaces is 0 25 the tension in the string is g 10 ms A 39 4 N B 24 8 N C 29 4 N

On applying a certain force a body of mass 5 kg moves on a horizontal surface with an acceleration of 1 ms 2 On doubling the force the acceleration becomes 3 ms 2 The coefficient of friction is g 10 ms 2 A 0 6 B 0 4 C 0 2 D 0 1

rough lane 8 inclination 300 slides down the plane with an acceleration g 4 where g is acceleration due gravity The coefficient of friction between th

A pushing force F is applied to a block of mass 2 3 kg as shown in the diagram What should be the maximum value of force so that the block does not move g 10 m s F 60

If cabin is descending vertical with acceleration a and action by mass M on floor of cabin is 9 Mg 10 then a equals to 1 g 2 Question Type Single Correct Type g 10 M 9 Cabin a

Consider the system of 2 pullies as shown in figure Both the pulleys are smooth and strings are light for at for at forstai facta stai 1 A m B m m c If popoloration of m was 5 m sec downward then find the value of Take g 10 m s

Block on the sphere shown in figure is in equilibrium it implies that net force is zero If sphere applies a force N of 3N on the block in the direction perpendicular 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 acts tangentially Assuming sphere is fixed smooth NK mg

The sliders A and B are connected by a light rigid bar of length 0 5 m and move with negligible friction in the horizontal slots shown For the position where XA 0 4 m the velocity of A is VA 0 9 m s to the right Deter the acceleration of each slider and the tension in the bar at this instant Acceleration of block B is equal to 7 5 m s downwards Acceleration of block A is 1 m s towards right Acceleration of block A is Tension in the bar is 15 11 1025 22 m s2 towards right N B 3 kg 0 5 m A 2 kg P 40 N Save a

2 Consider the system as shown in figure The body of mass M 3kg leans against wall P placed a the bottom of an inclined plane of an angle a 30 and a length s 10 m This body is connected by an inelastic string passed over an ideal pulley mounted at the top of the plane to another body of mass m 1 kg as shown What should be horizontal velocity in m sec of m so that the other the body M may detach from the wall P M a m

A hollow cylinder of mass M length L and radius R spinned about its centre with angular velocity was shown and placed on a smooth inclined plane Which of the following is correct