Newton's law of motion Questions and Answers

A wagon is going horizontally with an acceleration ao m s A system inside the wagon contains two blocks of mass M and m connected by a thread which passes over a pulley as shown in the figure all the surfaces are smooth M o m ao m s What is the total reaction force on the pulley as seen from the ground 2mM g 2mM g a b a c mM g a 2M m d mM g a 2m M M m

The acceleration of a particle starting from rest and moving along a straight line at any time t is given by a 4 2v where v is the velocity of particle at any time t The maximum velocity is 1 4 m s 2 2 m s

27 A patient s leg is kept at rest through the system of strings and massless rod as shown in 2 kg g 2 1 figure Given m 10 m s If net force applied by this system of strings and pulley and massless rod on the man s leg is xN then fill value of X 1 3 masses of pulley and string massless rod 37 45 m Neglect friction and 200M

2 For the given situation with what acceleratio the truck starts moving so that the 2 kg blod will fall from truck in 2 seconds 5m 1 10 m s 3 7 5 m s 2 kg 0 5 2 15 m s 4 5 m s

A block of mass M kept on a rough inclined plane of coefficient of static friction u 0 577 is pulled slowly up the plane by a thread forming an angle 0 with the plane as shown in the Figure The angle of incline is 30 M a 30 The tension required to pull the body with acceleration g up the incline if the string makes an angle 8 with the incline should be 0 is the angle for which tension in the string becomes minimum and T is the minimum tension 3T OfTo Reload Image

In the figure shown the coefficient of static friction between the block A of mass 20 kg and horizontal table is 0 2 What should be the minimum mass of hanging block just beyond which blocks start moving 20 kg p 02 8 1 2 kg 2 3 kg 3 4 kg 4 5 kg Two blocks A and B of masses 5 kg and 3 kg 2

18 In the arrangement as shown tension T is g 10 m s 1 50 N 3 50 N 10 kg 2 100 N 4 100 N 18 2 G

INSTITUTE MAMATHAN 26 What is the minimum value of F needed so that block begins to move upward on frictionless incline plane as shown 1 Mg tan 3 NIO Mg sin 0 1 sin 0 2 Mg cot 4 Mg sin COIN

1 1 g 2 0 4 g 3 0 6 g 4 0 8 g Three masses of 1 kg 6 kg and 3 kg are connected to each other with threads and are placed on a table as shown in figure T 2 6kg T 1kg 3kg What is the acceleration with which the system is moving Take g 10 ms 2 2 1 m 2 4 3 ms 2 1 zero 3 2 ms 2

Find out the tension in string which is connected with block Lift is accelerating downwards with acceleration of a 1 8 m s 1 12 8 N 2 16 N 3 18 2 N 4 Zero In the give figure find out force exerted by

How much force is needed to kick a 17 23 kg ball such that it moves with a velocity of 15 38 m s after 5 48 seconds Note Round off your final answer to two decimal places No unit is required for this question

In the system shown in figure block A is pulled towards the right at the speed v Find the velocity of block B at the instant when the string makes an angle with the horizontal Solution As block A moves closer block B will move down Break the string into intercepts as shown Here 1 1 2 Constant 1 0 VA COS VB 0 V V Cos 0 A A 1 A cose 0 V 1 B V B 1 B V

A block of mass m 1 kg is connected with an ideal string as shown in figure If the string is parallel to incline at the instant of release find the ratio of acceleration of M to that of m 2 kg instanteously Consider all the surface to be smooth M a 30

3 out from the wall 4 into the wall 17 In which of the following graphs the total change in momentum is zero 18 1 3 A A 2 A Ap 2 5 In the arrangement as shown tension T is g 10 m s

Mass M of hanging block in fig Which wi prevent block of mass m placed over triangular block of mass M from slipping take surface to be perfectly smooth strings ar pulley are massless 1 C M M m cot 0 1 M m tan 0 1 0 m 2 4 M M m cot 0 1 M m tan 0 1

17 Two blocks of masses 20kg 10kg are kept on a rough horizontal floor The coefficient of between the blocks are ground is u 0 2 The surface of contact of both blcoks are Horizontal forces of magnitude 20N and 60N are applied on both the blocks as shown in Match the following F 20N 20kg 10kg F 60N Column II Column I A Frictional forces acting on block of mass 10kg P has magnitude 20N B Frictional forces acting on block of mass 20kg Q has magnitude 40N C Normal reaction exerted by 20kg blcok D Net force acting 10kg block R is zero on 10kg block S is towards right block and 2

person of mass 60 kg is inside a lift of mass 40 kg and presses the button on control panel he lift starts moving upwards with an celeration 1 0 m s If g 10 ms the tension the supporting cable is 1 8600 N 3 11000 N Aavimum val 2 9680 N 4 1200 N otic fric friction is known mas

2 Consider the system shown in fig The pulley and the string are light and all the surfaces are frictionless The tension in the string is take g 10 m s DON m Ou 1 kg 3 1 kg m A 5 N

In the figure shown a body is acted upon by three forces such that it is in equilibrium Find the magnitude force F in N 5 N 53 Y 53 5 N X

A plank 1 m long is fixed with one end 28 cm above the level of the other end The top half of the plank is smooth and the bottom half is rough When a small block of mass m is released at the top it just reaches the bottom skipped B C D coefficient of friction between the block and the rough part of plank is 7 12 the coefficient of friction between the block and the rough part of plank is 1 2 Str on the rough part the reaction on the block is 24 25 mg on the rough part the reaction on the block is 28 100 mg

In the given figure V A B m m BA both masses always remain in same level after some time A is lower than B C after some time B is lower than A skipped 4

2 Two masses A and B of 10kg and 5kg respectively are connected with a string passing over a frictionless pulley fixed at the corner of a table as shown in figure The coefficient of friction of A with the table is 0 2 The minimum mass of C that may be placed on A to prevent it from moving is equal to C 10kg A A 15kg C 5kg 5 kg B B 10kg D zero

Sphere is placed between two smooth wedges and wedges are given velocities as shown in the diagram Velocity of centre of sphere in vertica direction will be 5 m s 1 10 m s 3 15 m s O 131 53 10 m s 53 2 5 m s 4 20 m s

om the top 50 m s as shown in 4 98 A shot of mass m is fired horizontally tower of height 100 m with a velocity u figure 4 154 At a distance 100 m from the foot of the tower a child throws a ball of same mass m in vertical direction with the same velocity u 50 m s He throws the ball such that the ball will collides with the shot in its path and merged with it making an object of mass 2 m Find the distance from the child where this object lands on ground 100 m 100 m Figure 4 154

Particles x of mass 4 kg and y of mass 9kg move directly towards each other and collide If Av is the change in velocity of x and Av is the change in the velocity of y The magnitude of the ratio is 94 M

BEER INSTITUTE STRIAN 38 Two bodies of mass 4kg and 6 kg are attached to the ends of a string passing over a pulley A 4 kg mass is attached to the table top by another string The tension in this string T is equal to 4kg 6kg 3 1 19 6 N 2 25 N 3 10 6 N 4 10 N 39 The acceleration of system of two bodies over 3

33 For the given figure what will be the contact 33 force applied by 6 kg block on 4 kg block 4kg 5kg 1 36 N 2 46 N 3 56 N 90N 5kg 6kg 10N 4 66 N lui 6 kg info eil 90N 1 36 N 5kg 6kg 2 46

3 12 N 4 96 N 10 Two men pull a rope from which a mass is hanging as shown Both apply a force of 100 N each What force should each apply to make the rope horizontal 30 30 1 200 N 2 400 N 3 600 N 4 Rope cannot become horizontal 12 2482 1 200 N 2 400 N 3 600 N 4 El 11 32 G telegram nestonpaper

Two blocks A and B having mass 3 kg and 2 kg respectively are connected by the massless string and placed on the smooth horizontal surface as shown in the figure If a force of 10 N is applied on block A then tension in the string connecting two blocks will be A 10 N 1 10 N 3 6 N 2 4 N 4 2 N

A 5 kg block has a uniform rope of mass 2 kg attached to its underside and a 3 kg block is suspended from the other end of the rope An external force of 80 N is applied on the 5kg block in upward direction as shown in figure If T is tension at mid point of rope and whole system is in mid air above the surface Find the T value of in N 4 F 80N 5kg 2kg

A block of metal weighing 2 kg is resting on a frictionless plane It is struck by a jet releasing water at a rate of 1 kg s and at a speed of 5 m s The initial acceleration of the block will be 1 2 5 m s 2 5 m s 3 10 m s 4 3 m s

equal weights of mass 2 kg each are hanging on a string passing over a fixed pulley as shown in fig What is the reaction of pulley on the support 1 28 6 N 3 26 8 N 64 B 2 53 33 N 4 19 6 N

34 A block of mass M is pulled by a rope of mass m by applying a force F at one end of the rope then what will be the tension at the middle point of the rope 1 BEER INSTITUTE THIAS 3 MF M m M M 2 M m m IL m 2 4 F mF M m m 2 M m M F

massless rods AB and AC as shown in the figure A vertical force P of magnitude 100 N is applied at point A of the frame P 70 145 C Suppose the force is P resolved parallel to the arms AB and AC of the frame The magnitude of the resolved component along the arm AC is xN The value of x to the nearest integer is Given sin 35 0 573 cos 35 0 819 sin 110 0 939 cos 110 0 342 Question Type Numerical Type

Two bodies of masses 15 kg and 40 kg are arranged as shown in fig if the pulleys and the table are perfectly smooth the accelerations of the 15 kg body is 1 3 8g 5 15 kg m s kg 2 8 11 g 4 5 9 g

H 2 A triangular block of mass M rests on a smooth surface as shown in figure A cubical block of mass m rests on the inclined surface If all surfaces are frictionless the force that must be applied to M so as to keep m stationary relative to M is A Mg tan 30 60 B mg tan 30 M 90 1 30 C M m g tan 30 D M m g cos 30 with borizontal can be kept stationary relative

4 Rope cannot become horizontal 11 A cricketer can throw a ball to a maximum horizontal distance of 100 m With the same effort he throws the ball vertically upwards What is the maximum height attained by the ball 1 50 m 2 60 m 3 70 m 4 80 m selegram 11 322 oil 12 33 dl ola 1 50 m 29 GE

All the strings springs and pulleys shown in figure are ideal Initially the system is in equilibrium and blocks are at rest Now the upper spring is cut The acceleration of block 1 just after cutting the upper spring is found y g m s Find y 1 mw BE elle 3 m 42m m 5

Illustrations vioolam A car starting from rest accelerates at the rate f through a distance S then continues at constant speed for Illustration 19 15 f time t and then comes to rest with retardation If the total distance travelled is 15S then calculate the value 2 of S in term of f and t Solution

figure a D surface m m 271 m b m m m a A The maximum acceleration of m is in case b B The maximum acceleration of m is in case c C The acceleration of m in case b can be more than acceleration due to gravity D The acceleration of m in case c can be more than acceleration due to gravity

3 TOT Determine the a of the blocks in the system shown in figure assuming that pulleys and strings are idea g 10 m s Onte onortw al basqa a TY 8 kg notinu 2 kg epniwollo a qurie vertions atrtpila A qiria sti savon mari anells A riv algne Josidua 80 en ainoo noosa av enigste ow 296m 58 00 WSA srit moni ahat sjalb er to beby 10

Find work done by external force to bring back the hanging part of chain on the tabletop alongwith the block The Chain is uniform having mass M and length L Home Work HW w Fe ext M L L 3 Vedan JE 3TE

The scale of the spring balance S shown is calibrated to read force in N If the elevator is going up with a acceleration of g 4 reading of the spring balance is found ng N If g denotes acceleration due to gravity what is numerical value of n 2 kg S 3 kg

2 In the rocket fuel is ejected with a velocity of 0 6 km s exerting a force of 6000 N on the rocket If the average density of exhaust while being ejected is 1 6 gm litre the rate of ejection of the fuel is 1 10000 lit s 2 6260 lit s 3 6 26 10 lit s 4 105 lit s a hall of mass 4

Block on the sphere shown in figure is in equillibrium 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 Hy NR mg

A batsman hits back a ball straight in the direction of the bowler without changing its initial speed of 12 ms 1 If the mass of the ball is 0 15 kg then the impulse imparted to the ball is 1 5 Ns 3 6 Ns 7 2 Ns

A toy cart of mass M is on a horizontal frictionless table as shown in figure A small block of mass m is at A Initially the system is at rest Block of mass m is released it slides on the cart without friction Find the time taken by the block to travel from B to C Given BC Land AD H

Find the time in which 2 kg mass will strikes the pulley after being released from rest 3kg A 10 sec 25m 2kg B 2 sec C 5 sec D 4 sec

A block of mass 4 kg lies over a horizontal surface Another block of mass 2 kg is placed over the first block The normal reaction between the lower block and ground surface is g 1 ms 2 O 40 N O 60 N 20 N 10 N

d and the collides and 3 kg 4 75 Nbeads are resting on a smooth horizontal wire which is circular at the end with radius r as shown in figure The masses m 2 1 respectively Find the of the beads are m m 2 m 4 minimum velocity which should be imparted to the first bead of mass m such that the nth bead will fall in the tank shown in figure 4 148 y at rest at rest ind the ed h is ack OO 2 n 1 Figure 4 148