Newton's law of motion Questions and Answers

A small cart with a ball suspended from a thread moves with a velocity V toward an smooth inclined surface The thread will be deflected from the vertical When the cart begins to run up the inclined surface A In back ward direction C No deflection Vo 77 B In forward direction D Data insufficient

pulleys in which all strings are attached to a beam the highest string after passing over a fixed pulley has a mass 1 4 kg attached to it and the lowest pulley has a mass of 13 kg hung on to it The acceleration of the larger mass is in m s Beam

6 8 A rubber cord has a cross sectional area 10 m and total unstretched length 0 1 m It is stretched to 0 125 m and then released to project a particle of mass 5 0 g The velocity of projection is Given Young s modulus of rubber Y 5 x 108 N m a 45 m s b 30 m s 25 m s d 15 m s

Q2 Two particles of mass m each are tied at the ends of a light string of length 2a The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance a from the center P see figure Now the mid point of the string is pulled vertically upwards with a small but constant force F As a result the particles move towards each other on the surface The magnitude of acceleration when the separation between them becomes 2 r is 2007 A F FE M11 B D F 2m F F P a a x m

A block is hanging at one end of the massless rope passing over a fixed smooth pulley From other end of the rope a man of same mass climbs with ar acceleration x relative to the acceleration of rope which is a The value lolli

A man of mass 60 kg is standing inside a box of mass 20 kg Man pull a string which supports the box as show figure If given system is at rest then find out 1 Tension in string 2 Force exerted by man on base N 2 m

3 15 75 30 60 45 4 30 60 15 45 75 39 The tension T in the string shown in figure is 1 50 N 2 Zero 3 35 3N 4 3 1 50N 10kg 30 T 0 7 3 15 75 30 60 45 4 30 60 150 45 75 39 ff 1 50 N 1 3 35 3N 4 3 1 50N 10kg 30 u 0 7 www

Two blocks A and B are connected by a light spring They are of masses 1 0 kg and 2 0 kg respectively The system is placed on a smooth horizontal plane and the block B is pulled by a horizontal force of 10 N At the instant shown in the figure acceleration of the block A is observed to be 2 0 m s towards right Acceleration of the block B at this instant is B A 0000000000 Question Type Single Correct Type 1 0 0 m s 22 0 m s 3 3 0 m s F 4 4 0 m s

37 A plank is resting on a horizontal ground in the northern hemisphere of the Earth at a 45 latitude Let the angular speed of the Earth be w and its radius r The magnitude of the frictional force on the plank will be a mr 0 3 2 mr 0 b 2 mr 0 2 d Zero

Two blocks of masses 2m and 3m are connected through a string which passes over a pulley disc of mass m and radius R as shown in figure If system is released from rest and string does not slip on the pulley then angular acceleration of the pulley is Tz 3m 2 23 29 70 Smooth 3ml 2m 4 g 2 11R Zeg X 2mg 20

onkey of mass 40 kg climbs on a massless rope which 184 can stand a maximum tension of 500 N In which of the following case will the rope break Take g 10 ms 2 500 40 a g 580 69 12 5 0 The monkey climbs up with an acceleration of 5 ms 2 The monkey climbs down with an acceleration of 5 ms 2 3 The monkey climbs up with a uniform speed of 5 ms 4 The monkey falls down the rope freely under gravity fubfta fff t ge arquit Take g 10 ms 500 40 g a 12 Mechanics upto NLM Friction 1 5 2 5 ms Pe T 3 4 4 5 ms 4 4 t

connected by a string passing over a pulley as shown If the coefficient of friction be 0 15 then the minimum weight that may be placed on m2 to stop motion is Im 10kg m T m 5kg

A body travels uniformly a distance of 13 8 0 2 m in a time 4 0 0 3 s The velocity of the body within error limits is 1 3 45 0 2 ms 2 3 45 0 3 ms 1 3 3 45 0 4 ms 1 4 3 45 0 5 ms 1

59 Figure shows two cases In first case a spring spring constant K is pulled by two equal and opposite forces F at both ends and in second case is pulled by a force Fat one end Extensions x in the springs will be FMF case 1 MF case 2 1 In both cases x 2 In both cases X 2F 3 In first case x K F 0 nel n 1 8 vdbshogo2FW Iripiew to Xbold AF K beniloni in second case X Sign Thewone K 918 Seprinta erti ni noienet 10 out ovloed 10 bris Aap Fizant olenet erle2F 4 In first case X in second case X ak

11 A force can generate an acceleration of 4 m s in an object 4 Zero of mass m The same force can generate an acceleration of 6 m s2 in an object of mass m If same force is applied on an object of mass m m then acceleration of object will be m s 6m 5 2 1 10 m s 2 2 m s 3 2 4 m s 4 5 4 m s A body of mass 4 kg is accelerated upon by E 4m s ma F m tm 1 onstant JEJ 1 10 m s m 2 2 m s 3 2 4 m s 4 5 4 m s A ko 4 m s 6 m s af set gen an m m 5045 at an afforda F m

Two bodies of masses 4kg and 6kg are attached to the ends of a string passing over a pulley The 4kg mass is attached to the table top by another string The magnitude of tension in this string T is equal to g 10m s A B C D 10 N 10 6 N 25 N 20 N 4kg T T 6kg

3 A 3 5 kg computer printer is pushed at a constant velocity across a desk with a horizontal force The coefficient of kinetic friction between the printer and the desk is 0 36 Draw a FBD of the printer as it is being pushed Be sure to label your forces appropriately and to include values

AB is stationary curved surface blade A stream line water impinges on the curved surface The speed of stream line water is u both before and after it strikes the curved surface of the blade The mass flow rate of water per unit time is u Find the force exerted by water on the blade in Newton Given u 2 2 m s 200 gm sec

A container of mass 200 Kg is moving towards right by applying a constant horizontal force 100 N Initial velocity of container is zero Sand is falling in container with a constant rate of 1 kg sec with the help of a fixed cone as shown in the figure Find the velocity of the container in m s at t 100 sec Flexed cone 1

15 A bullet is moving at a speed of 367 m s when it embeds into a lump of moist clay The bullet penetrates for a distance of 0 0621 m Determine the acceleration of the bullet while moving into the clay Assume a uniform acceleration

12 A plank with a box on it at one end is gradually raised about the other end As the angle of inclination with the horizonta reaches 30 the box starts to slip and slide 4 0 m down the plank in 4 0 s The coefficients of static and kinetic friction between the box and the plank will be CBSE AIPMT 201 respectively a 0 6 and 0 6 mg 0 b 0 6 and 0 5 04 and 0 2

A small mass slides down an inclined plane of inclination 0 with the horizontal The co efficier friction is ox where x is the distance through which the mass slides down and uo a constant T the speed is maximum after the mass covers a distance of cose sine tane 2 3 Ho Ho H 2tane

1 A block A of mass m rests on a horizontal table A light string connected to it passes over a frictionless pulley at the edge of table and from its other end another block B of mass m is suspended The coefficient of kinetic friction between the block and the table is u When the block A is sliding on the table the tension in the string is a m H m my m m m 1 g m m b d CBSE AIPMT 2015 m Hkm g m m m m 1 H g m m

55 A ball of weight W rests upon a smooth horizontal plane and has attached to its center two strings AB and AC that pass over frictionless pulleys at B and C The other ends of the strings carry loads P and Q respectively as shown in the figure If the string AB is horizontal the angle a that the string AC makes with the horizontal when the ball is in th state of equilibrium is SINESSBANKE a a sin TO P C b a cos P POLL La Q c sin 2 cor 1 Q

28 A system of blocks A and B of masses m and m2 connected by a spring of force constant k is placed on a spring of force constant k which rests on the ground Both the springs are vertical and the whole system is in equilibrium Find increment in gravitational potential energy of the system in lifting the block A upwards until the lower spring becomes relaxed B F k

In the given system force constant of the spring is k mass of the fixed pulley is negligible and mass of movable pulley is m If the moment of inertia of the movable pulley is negligible and the block of mass m is pulled down from its equilibrium position find the time period of free oscillations m1 00 m2

Classical Mechanics Study 1 Using conservation of momentum show that the final velocity of a rocket is related to its initi velocity exhaust velocity initial mass and final mass as follows mo v Vex In Vo

3 A mass m is attached to an elastic cord model as a spring with spring constant k and placed on a ramp that makes an angle with the ground The equilibrium length of the cord is lo when there is the mass m attached Assume the ramp is frictionless but that there is linear air drag Assume that the system is overdamped The mass starts from the equilibrium position i e the length of the cord starts at lo and has an initial velocity of Vo What is the position of the mass as a function of time If you wait a very long time what will the final position of the mass be

A body mass 8 kg placed on a smooth horizontal table is connected by a light string passing over a pulley to a hanging body of mass 2 kg Find the acceleration of the masses and the tension in the string g 10m s 8 kg T T 2 kg

0 In the figure shown the time period and the amplitude respectively when m is released from rest and the spring is relaxed is the inclined plane is smooth k mm O2 O 2 k Mark Tor Review O2 K Fixed mg sin e k msine 2mg sine k k 02 46 hr min m mg cose k

17 A body of mass 5 kg is moving with velocity of v 21 6j m s at t 0 s After time t 2 s velocity of body is 10i 61 then change in momentum of body is 1 40 kg m s 3 30 kg m s 2 201 kg m s 4 50i 30 kg m s through the hole as shown in diagram then aft

15 A ball of mass 1 kg is dropped from 20 m height on ground and it rebounds to height 5 m Find magnitude of change in momentum during its collision with the ground Take g 10 m s tion of Newton s Second Law of Motion Cricket player lowers his hand while catching the ball The player increases the time during which the high velocity of moving ball reduces to zero

3 A rope is wound around a hollow cylinder of mass 3 kg and radius 40 cm What is the angular acceleration of the cylinder if the rope is pulled with a force of 30 N NEET 2017 a 25 m s c 25 rad s b 0 25 rad s d 5 m s

Two vectors A and B are defined as A ai and B a cos wt sinwtj where a is a constant 75 and w rads If B 3 A B at 6 time T for the first time the value of T in seconds is

The mass of the body which is hanging on the rope attached to the movable pulley is four times as much as the mass of the body which is fixed to the ground At a given instant the fixed body is released If the initial acceleration of block m in m s2 is 2x then find the value of x The mass of the pulleys and the ropes are negligible 4m

In figure all contacts are smooth and string spring are light Blocks A B C have same mass of 1kg Initially A is held by some one and B C are at rest Determine acceleration of block C in m s just after block A is released Take g 10 m s B A relle C

A cubical block of mass m is sliding down the smooth incline of a wedge of mass M which is kept on a rough horizontal surface The minimum coefficient of friction between the wedge and the horizontal surface for it the wedge to remain stationary is 0 m M

In the figure shown a ball of mass m collides perpendicularly on a smooth stationary wedge of mass M kept on a smooth horizontal plane If the coefficient of restitution of collision is e then determine the velocity of the wedge after collision M 0 Vo m

A 1000 kg elevator is pulled up by a metallic wire that has maximur stress equal to 2 x 10 N m If the diameter of the wire is 0 1 m th the maximum safe acceleration of the elevator will be 1 9 m s 16 m s O 5 7 m s O 21 m s

A fixed wedge with both surface inclined at 45 to the horizontal as shown in the figure A particle P of mass m is held on the smooth plane by a right string which passes over a smooth pulley A and attached to a particle of mass 3 m which rests on a rough plane The system is released from rest Given that the acceleration of each particle is of magnitude 9 5 2 then tension in the string is Smooth Rough 45 fixed 45

A boy holds a hydrogen filled balloon with a string He is sitting in a train moving with uniform velocity on a straight track The string is vertical On applying brakes the balloon will A be thrown forward Bbe thrown backward C remain vertical ce D fall downwards

D64 The weights of the blocks A and B as shown are 200 lbf and 52 lbf respectively The system is initially at rest and s 0 4 between all surfaces of contact Determine the magnitude of the horizontal force P that will cause motion of the block A to impend

If a rifle is fixed on the ground and fired which of the following statement is CORRECT A B The bullet will not return to the ground Newton s third law of motion is not obeyed Newton s third law of motion is obeyed Recoil force doesn t act on rifle e D

4 None of these 16 Assuming that the block is always remains horizontal hence the acceleration of B is 12 m s A 1 6 m s 2 2 m s 3 4 m s 4 None of these B

S A plate bent at right angles along its centre line is placed onto a horizontal fixed cylinder of radius R as shown in the figure How large does the coefficient of static friction us between the cylinder and the plate need to be if the plate is not to slip off the cylinder

2 A balloon with mass 20 kg is moving downward with an acceleration 2 2 m s2 What mass Am of its contents be removed so that it starts moving up with same acceleration g 9 8 m s O 2 66 kg O 7 33 kg O 4 66 kg O 5 33 kg

A uniform triangular wedge of mass M is kept on smooth horizontal surface A horizontal force F applied on the wedge then net force on the upper portion ABC is AB 1 2 and neglect any effect rotation My A F 4 F smooth C 90 fayllar au R ABC AB 1 2 ts 1 AB is horizontal line B B F 3 F fachall C F 90 AB I B D None

Slider block A moves to the right with constant velocity 6 m s in the arrangement as shown in the figure C and D are points on the string If and are the velocities of B C and D respectively then choose correct option Ai e f a far af B C a D 6 m s engar ma se va farget af A Vc Vo 4 V C V Vc Vo 2 V 6m s B B Ve Vc Ve Vo V D Vc 2

a massless spring as shown 000000 a mg b 2 mg c 3 mg d 4 mg m m A weight W is put on the upper plate which compresses the spring further When W is removed the entire assembly jumps up The minimum weight W needed for the assembly to jump up when the weight is removed is just more than

When one of the slits of Young s experiment is covered with a transparent sheet of thickness 4 8 mm the central fringe shifts to a position originally occupied by the 30th bright fringe What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe a 38 mm b 1 6 mm c 7 6 mm d 32 mm