Newton's law of motion Questions and Answers

A mass M of 100 kg is suspended with the us of strings A B and C as shown in the Fig where W is the vertical wall and R is a rigi horizontal rod The tension in the string B is R W 1 100 g N 90 3 100 2gN B A 4 2 Zero 100 45 C M 100kg gN

A 470 g lead ball is launched at 60 angle above the horizontal with an initial speed of 100 m s directly towards a target on a vertical cliff wall which is 150 m away as shown in the figure Ball 100m s 60 150m Target A Time taken by ball to hit the cliff is 1 5 second B Time taken by ball to hit the cliff is 0 75 second C The distance by which lead ball misses the target when it hits the wall is 2 81 m D The distance by which lead ball misses the target when it hits the wall is 11 25 m

d both a and c are corr M 3 kg and 4 Two blocks of masses m 2 kg are in contact on a horizontal table A constant horizontal force F 5 N is applied to block M as shown There is a constant frictional force of 2 N between the table and the block m but no frictional force between the IT table and the first block M then acceleration of the two blocks is a 0 4 ms 2 2 c 0 8 ins F M m b 0 6 ms 2 d 1 ms 2

View In English 50 kg man stands on a spring scale in the lift At some instant he finds scale reading has changed from 60 kg to 50 kg for a while and then comes back to the original mark What ould we conclude 1 2 3 4 Answer 3 wer 4 incorrect The lift was in constant motion upwards The lift was in constant motion downwards The lift while in constant motion upwards is stopped suddenly The lift while in constant motion downwards is suddenly stopped to Bookmark List 41 4 A and Care of the same length while B is smaller than A and D is larger th Right Answer 21 Your Answer 3 14

spherical ball of radius r and having mass m is placed on the smooth movable wedge of mass M and having a semicircular track of radius R Initially the system is released from rest There is no friction anywhere Then choose the correct option s M mmmm Normal force exerted by the ball on the wedge when ball reaches the bottom most point of the track mg 3 2m 0 A B 0 C m D 0 Normal force exerted by the ball on the wedge when ball reaches the bottom most point of the mg 3 track mg m 2M radius of curvature of the ball at the bottom most point is radius of curvature of the ball at the bottom most point R r 1 m M 2 R r 1 m M

A car turns a corner on a road at a constant speed If the coefficient of friction is 0 4 and the radius of arc is 36 m then the maximum speed with which it can turn is 1 10 m s 3 15 m s 2 12 m s 4 18 m s

SolveLancer Test For the given configuration minimum value of force F is applied such that slipping starts between B and C Calculate the acceleration of block B for this condition and the value of F 0 1 0 5 0 1 a 15 m s 250 N b 10 m s 200 N c 5 m s 260 N d 15 m s 260 N A 10 kg B 10 kg C 5 kg SolveLancer Test

8 Figure 7 21a shows four situations in which a horizontal force acts on the same block which is initially at rest The force magnitudes are F F 2F 2F The horizontal component v of the block s ve locity is shown in Fig 7 21b for the four situations a Which plot in Fig 7 21b best corresponds to which force in Fig 7 21a b Which D A C F B a K H

A rod AB of mass m is suspended by two massless spring of equal spring constant k One of the springs is cut Immediately after cutting the spring X component of the acceleration of COM of N the rod is g Find N k quell oooo

2 The 400kg mine car shown in Fig Q2 is hoisted up the incline using the cable and motor M For a short time the force in the cable is F 3200 t N where t is in seconds If the car has an initial velocity of v 2m s when t 0 sec and s 0 Determine the velocity v and displacement s when t 2 sec Make sure to draw appropriate FBD and Kinetic diagram note g 9 81 m s 20 points 17

As shown in Fig Q1 in the test of an energy absorbing bumper a 2800 lb car is driven into a barrier at 5 mi h The duration of the impact is 0 4 seconds When the car rebounds from the barrier the magnitude of its velocity is 1 5 mi h Note 1 mph 1 4667 ft sec 20 points a What is the magnitude of the average horizontal force exerted on the car during the impact b What is the average deceleration of the car during the impact

The active gravitational mass m of a particle is an attribute that enables it to establish a gravitational field in space whereas the passive gravitational mass m is an attribute that enables the particle to respond to this field a Write Newton s law of universal gravitation in terms of the relevant active and passive gravitational masses b Show that the third law of motion makes it unnecessary to distinguish between active and passive gravitational mass

29 Figure shows the position time x t graph of one dimensional motion of a body of mass 500 g What is the time interval between two consecutive impulses received by the body x m 2 M 0 2 4 6 8 10 12 t s 29 fa fr at 1

1 A stone is dropped from the top of a tall cliff and n seconds later another stone is thrown vertically downwards with a velocity u Then the second stone overtakes the first below the top of the cliff at a distance given by gn nu 0 2 1 4 8 u gn c u n g 2 bol 2 u gn b ool g d n 60 2 u 2 2 u gn gn u gn u

A 5 A body is hanging over a pulley inside a ca through a string The second end of the string i in the hand of a person standing in the car The car is moving with constant acceleration a directed horizontally as shown in figure Other end of the string is pulled with constant acceleration a vertically The tension in the string is equa to m 2 2 1 m g a car ja a 2 m g a ma

9 Suppose that the particle in above exercise is an electron projected with velocity v 20 x 10 m s If electric field between the plates separated by 0 5 cm is 9 1x 10 N C at what maximum distance will the electron strike the above 19 kg C plate e 1 6x 107 C me 9 1x 10 31 B

A block of mass m is pulled by horizontal constant force F 5 mg over a rough surface of coefficient of friction as shown Initially spring was at its natural length the position where block will finally come to rest is N times of 5 mg where N is k k mooooo m F

D None of these A gun which fires small balls of mass 20 gm is firing 20 balls per second on the smooth horizontal table surface ABCD If the collision is perfectly elastic and balls are striking at the centre of table with a speed 5 m s at an angle of 60 with the vertical just before collision then force exerted by one of the leg on ground is assume total weight of the table is 0 2 kg and g 10 m s A 0 5 N C 0 25 N B 1 N D 0 75 N B

E 100 N C A Smooth Consider the experimental set up in which an object of mass 2 kg is placed at point A and at t 0 the electric field is switched on The electric field is switched off at t 2 sec The linear momentum of the object at this instance is Given Charge on object 5C SolveLancer Test a 250 kg m s b 100 kg m s c 152 kg m s d 252 kg m s

Mass of car 10 kg 2 kg F Smooth A car of mass 10 kg is moving under action of force F Block A of mass 2 kg is kept in car as sh apply Newton s law on A in the frame of reference of car a pseudo force of 21 4j is to be ass acting on it What is the value of F acting on system assume No slipping between block A an SolveLancer Test a 10 20j b 101 20j c 12i 24j d 121 24j

The escape velocity of a particle of mass m varies as 1 m 3 mo 2 m 4 m 138 A particle starting from the point 1 2 moves in a straight line in XY plane Its coordinates at a later time are 2 3 The path of the particle makes with x axis an angle of 1 30 2 45 3 60 neet prep frictionless table The hand H is slowing them down T mass of A is larger than the mass of B Rank in ord from largest to smallest the horizontal forces on A and H 1 FB on H FH on B FA on B FB on A V MA MB A Slowing B H High Yielding Test Series Part Test 5 Half XIth Contact Number 9667591930 85275217 IIIII Frictionless surface

The 1 0 kg block in the figure is tied to the wall with a rope It sits on top of the 2 0 kg block The lower block is pulled to the right with a tension force of 20 N The coefficient of kinetic friction at both the lower and upper surfaces of the 2 0 kg block is k 0 32 Figure 1 You may want to review Pages 169 172 For general problem solving tips and strategies for this topic you may want to view a Video Tutor Solution of Car on rolling board Figure 1 0 kg 1 of 1 20 N Part A What is the tension in the rope holding the 1 0 kg block to the wall Express your answer with the appropriate units Value Submit A Part B Units Request Answer Value What is the acceleration of the 2 0 kg block Express your answer with the appropriate units avea Units

The velocity time graph of a particle moving along a straight line is shown in the figure given below 2 v m s 1 0 1 2 The displacement of the particle in 5 second is 1 0 5 m 3 2 m 1 2 3 2 1 m 4 4 m B E D G 4 5 C t s

b 300 N d 30 N c 3 N 27 A golf ball of mass 100 g at rest is hit with a striker Find the impulse of the hit if the ball stops after traveling a horizontal distance of 100 m with a uniform retardation of 5 m s a 0 3 Ns c 3 16 Ns b 0 1 Ns d 0 9 Ns

v m s 4 3 2 1 tt A 1 s B 3 s C 4 s D 5 s 1 2 3 4 5 6 7 8 t s O 3 The velocity v of an elevator moving upward between adjacent floors is shown as a function of time t in the graph above At which of the following times is the force exerted by the elevator floor on a passenger the least

An elevator starts from rest with a constant 1 upward acceleration It moves 2m in the first 0 6 s A passanger in the elevator is holding a 3kg package by a vertical string When the elevator is moving the tension in the string is 1 4N 2 62 7N 3 29 4 N 4 20 6N

A small ball on a frictionless horizontal surface moves towards right with a velocity v It collides with the wall and returns back If the average speed for first to and fro motion of the 2 3 ball is restitution of impact is m 1 0 5 3 0 25 v then the coefficient of A 2 0 1 4 0 75 B

In the adjacent figure a wedge B of mass 2m is lying at rest on a horizontal surface The wedge has a cavity which is the portion of a sphere of radius R A small sphere A of mass m is released from the top edge of the cavity to slide down All surfaces are smooth Point A is at the same height as centre of cavity Choose the correct option s S B The maximum speed acquired by the sphere is 4gR 3 The maximum height from the bottom of the circular path to which the sphere will rise after breaking off the wedge is 10R 11 The wedge will acquire its maximum speed when the sphere is about to leave it gR

Two masses of 1 kg and 5 kg are attached to the ends of a massless string passing over a pulley of negligible weight The pulley itself is attached to a light spring balance as shown in figure The masses start moving during this interval the reading of spring balance will be wwwwwwwwww O more than 6 kg O less than 6 kg O equal to 6 kg O none of the above 1kg 5kg

1 A body of mass 2 kg moving on a horizontal surface with an initial velocity of 4 m s comes to rest after 2 sec If one wants to keep this body moving on the same surface with a velocity of 4 m s the force required is 8 N 2 4 N 1 Tu 3 zero 4 2 N

5 For the given figure two blocks of equal mass m are connected by a light string that passes over a smooth pulley The block A is connected by spring constant k Initially spring is relaxed Then the block A is slowly pulled down a distance x and released The magnitude of accelerations of the left and the right blocks and az immediately after releasing are a respectively 19 A m E 0000 m B Now choose the correct options a a a b a a if ks 2mg

A basket and its contents have mass M A monkey of mass 2M grabs the other end of the rope and very quickly almost instantaneously accelerates by pulling hard on the rope until he is moving with a constant speed of Vm r 2ft s measured relative to the rope The monkey then continues climbing at this constant rate relative to the rope for 3 seconds How fast is the basket rising at the end of the 3 seconds Neglect the mass of the pulley and the rope given g 32ft s 0 4ft

A rough vertical board has an acceleration a such that a 2 kg block pressing against it does not fall down For this situation the possible value of the coefficient of friction between the block and the board can be g acceleration due to gravity at 1 2g a 2 kg 2 g 2a 2a mu 913 P P

D The two wires shown in figure are made of the same material which has a breaking stress of 8 x 108 N m The area of cross section of the upper wire is 0 006 cm2 and that of the lower wire is 0 003 cm2 The mass m 10 kg m 20 kg and the hanger is light The maximum load that can be put on the hanger without breaking a wire is 1 14 kg www EA 2 1 4 kg

Two spheres having masses m and m are kept on an inclined plane as shown Both of them are in equilibrium What is a necessary condition for this 44 is coefficient of friction between m and inclined plane and u is coefficient of friction between m and inclined plane 1 m m O 2 m m2 m m 3 m m 4 m 2 m

is zer 3 Direction of IR remains unchanged and VR is maximum at t 0 5 4 At t 0 25 direction of IR reverses and VR is maximum A 60 HP electric motor lifts an elevator having a maximum total load capacity of 2000 kg If 9 the frictional force on the elevator is 4000 N the speed of the elevator at full load is close to 1 HP 746 W g 10 ms 2 1 1 7 ms 1 3 1 9 ms 1 2 2 0 ms 1 0 4 1 5 ms 1 1 3 If we n compou and an length 1 22 3 3

on a horizontal surface The 5 0 kg block is pulled to the right with a force F as shown in Fig 39 The coefficient of static friction between all surfaces is 0 60 and the kinetic coeffi cient is 0 40 a What is the minimum value of F needed to move the two blocks b If the force is 10 greater than your answer for a what is the acceleration of each block 3 0 kg 5 0 kg F

140 g baseball is moving horizontally to the right at 40 s when it is hit by the bat The ball flies off to the left at m s at an angle of 25 above the horizontal What is the magnitude of the impulse that the bat delivers to the ball Express your answer to two significant figures and include the appropriate units J Submit Part B HA Value Ti Request Answer Units What is the direction of the impulse that the bat delivers to the ball Express your answer to two significant figures and include the appropriate units A

A uniform rod AB of mass 5 kg and length 10m is hinged at A A block of mass 10 kg is hanging with a string and other end of the string is attached to a middle point of the rod passes over a smooth pulley as shown in the figure Find the value of cos 0 2 10 kg A 5 m 0 10 m

32 A mass m is supported by a massless string wound arou a uniform hollow cylinder of mass m and radius R If t string does not slip on the cylinder with what accelerati will the mass fall or release JEE Main 201 a 6 2g 3 g N 1020 2 5g 6 c d g A blod C m R m

A particle is moving with a uniform speed in a circular orbi of radius R in a central force inversely proportional to th nth power of R If the period of rotation of the particle is I then JEE Main 2018 a To R 2 for any n 6 c Tx R n 1 2 b To Rn 2 1 d To Rn 2

d It hits the gro 4 ms 13 Three masses of 1 kg 6 kg and 3 kg are connected to each other with massless strings and are placed on a table as shown in figure 6 kg T 1 kg 10 m s the If g system is moving is a 6 ms2 c 1 ms2 3 kg acceleration with which the b 2 ms2 d 4 ms 2 tal nine 20

Two blocks of masses 7 kg and 5 kg are connected by a rope of mass 4 kg The system is pulled up with a force of 240 N as shown in figure The tension in the rope at its midpoint A is a 105 N c 240 N b 270 N d 50 N UP CPMT 2401 7 kg 5 kg

When mass is fixed and velocity is constant then it is valid for Newton s 2 nd law of motion And when mass is variable and comparable to each other and velocity must change then Newton 2 nd law of motion is not valid 10 38 AM

A 64 9 N diver stands at the edge of a 5 54 m diving board with a mass of 6 25 kg which is connected to two narrow pillars 2 00 m apart as shown Find the magnitude of the force exerted on the diving board by pillar A Round your answer to the nearest whole number A 2 00 m B L

THERMAL EQUILIBRIUM In mechanics the term Equilibrium means that the net external force ar torque on a system are zero But in thermodynamics the term therm equilibrium means temperature of two systems are equal and there is r exchange of heat if put in contact

ball A Rolls at a constant speed of 0 25 m s on a table of 0 90 m above the floor and ball B Rolls on the floor directly under the first ball with the same speed and same direction When ball a hits the floor how far from the point directly below the edge of the table where the ball be

d 9 s 212 The maximum range of a projectile is 500 m If the particle e 7 s is thrown up a plane inclined at an angle of 30 with the same speed the distance covered by it along the inclined plane will be a 250 m b 500 m c 750 m d 100 m 213 A proiectila

What force does a trampoline have to apply to a 45 0 kg gymnast to accelerate her straight up at 7 46 m s Note that the answer is independent of the velocity of the gymnast she can be moving either up or down or be stationary

8 A man pushes a truck initially at rest and weighing 5 tonnes along horizontal rail with a steady force of 400N The resistance to motion amounts to 60N per tonne The velocity of the truck at the end of 30 sec is 1 0 6 m s 2 0 3 m s 3 0 2 m s 4 none