Newton's law of motion Questions and Answers

Two small identical balls each of mass 0 20 g carry identical charges and are suspended by two threads of equal lengths The balls position themselves at equilibrium such that the angle between the threads is 60 If the distance between the balls is 0 5 m find the charge on each ball

100 coplanar forces each equal to 10 N act or a body Each force makes angle r 50 with the preceding force What is the resultant of the forces 1 1000 N 3 250 N 2 500 N 4 Zero

39 The block Q moves to the right with a constant velocity v as shown in figu P with respect to Q is assume all pulleys and strings are ideal 1 1 V towards left 3 2 towards right 2 Vo towards right 2 4 2o towards left P Q Vo

3 55 A ball is allowed to fall from top of a building If t is 1 time taken to fall first th of its height and t is time 4 taken to fall last t lt is th of its height then 4

A body starts from rest what is the ratio of the distance travelled by the body during the 4th and 3rd second a c 75 73 b d 5737 1993

What is the minimum acceleration with which bar A should be shifted horizontally to keep the bodies 1 and 2 stationary relative to the bar The masses of the bodies are equal and the coefficient of friction between the bar and the bodies equal to u The masses of the pulley and the threads are negligible while the friction in the pulley is absent see in fig A 2

Consider the situation shown in figure 6 E2 Calculate a the acceleration of the 10 kg blocks b the tension in the string connecting the 10 kg blocks and c the tension in the string attached to 0 50 kg 1 0 kg 0 2 1 0 kg 0 2 Figure 6 E2 0 5 kg

3 Zero An object with a mass 10 kg moves at a constant velocity of 10 m sec A constant force then acts for 4 second on the object and gives it a speed of 2 m sec in opposite direction The acceleration produced in it is 1 3 m sec 2 3 m sec In the above question the force acting on the object is 1 30 N 2 30 N In the above question the impulse acting on the object is 1 120 newton x sec 2 120 newtont sec 3 30 newton x sec 4 30 newton x sec A machine gun is mounted on a 2000 kg car on a horizontal frictionless surface At some instant 3 0 3 m sec 3 3 N 4 4 0 3 m sec 3 N

Two blocks which are connected to each other by means of a massless string are placed on two inclined planes as shown in figure After releasing from rest the magnitude of acceleration of the centre of mass of both the blocks is g 10 m s m 53 1 1 m s 3 2 m s m Fixed 37 2 2 m s 4 Zero

In the shown figure blocks A and B are of mass 1kg each and surfaces are all smooth Spring constant is k 60 N cm The system is in equilibrium The minimum mass of block C for which when block C is suddenly removed the block A leaves contact from support is ond S A 000000 BC 37

6 In the arrangement shown the 2 kg block is held to keep the system at rest The string and pull are ideal When the 2 kg block is set free by what amount the tension in the string changes g 10 m s A Increase of 12 N C Increase of 18 N 2kg 30 3 kg B Decrease of 12 N D Decrease of 18 N

vy cart is pulled by a constant force F along a horizontal track with the help over a fixed pulley as shown in the figure Assume the tension in the rope and the frictional forces or the cart remain constant and consider motion of the cart until it reaches vertically below the pulley As the cart moves to the right its acceleration A decreases B increases C remains constant D is zero

24 A flexible chain of weight W hangs between two fixed points A B which are at the same horizon level The inclination of the chain with the horizontal at both the points of support is 8 What is t tension of the chain at the mid point W A cosec 0 W 2 B tan e C W cor 9 D none

II Match the following 1 Newton s I law propulsion of a rocket 2 Newton s II law stable equilibrium of a body 3 Newton s III law see saw gears and steering wheel RNAL US 4 Laws of conservation of linear momentum flying nature of bird 5 Torque law of force FAR

Two particles A and B are connected by a straight rigid rod The rod slides down along the mutually perpendicular rails as shown in Figure 4 Q7 If Fig 4 07 the velocity of B to the right is 10 ms what is the velocity of A when 0 30 B

B d 1 2 2 In the setup shown a thread is taut between a nail A on a wall and a nail B on an inclined plane as shown in the figure You can change the length of the thread by changing location of the nail B A bead that can slide on the thread without friction is released from the nail A What should the length of the thread be so that the bead reaches the nail B in shortest time a h c h sec 0 50 b h cos 0 d h cosAsec 0 58

26 A man is raising himself and the crate on which he stands with an acceleration of 5 m s2 by a massless rope and pulley arrangement Mass of the man is 100kg and that of the crate is 50kg If g 10 m s then the tension in the rope is

The small spherical balls are free to move on the inner surface of the rotating spherical chamber of radius R 0 2 m If the balls reach a steady state at angular position 0 45 the angular speed of device is a 8 rad s b 2 rad s c 3 64 rad s d 9 34 rad s

The below figure is the part of a horizontally stretched net Section AB is stretched with a force of 10 N The tensions in the section BC and BF are Eth 150 150 120 NEC 90 2 0 120 120 a 10 N 11 N 10 N 10 N d cannot be calculated due to insufficient date b 10 N 6 N 5

A rectangular box lies on a rough inclined surface The coefficient of friction between the surface and the box is u Let the mass of the box be m The force acting on the box down the plane if the angle of incli nation of the plane is increased to a 0 is 1 mg Sin a u Cos a 2 mg Cos 0

A boat of mass M moving with the help of an ideal string which is being pulled with 5 m s as shown in figure A Constant resistive force R is applied by the water opposite to the direction o motion of boat Then at the given instant when string makes an angle with the horizontal Assume that boat does not lift up 5ms constant 09 M 8 Resistive force R constant a Find the acceleration of the boat at the given instant b Find the tension in the string at the given instant 10m 177

1 A man is swinging on a swing made of 2 ropes of equal length L and in direction perpendicular to the plane of paper The time period of the small oscillations about the mean position is A 2 L 2g B 2n 3 L 2g L M L C 2 2 3g D T 10 0 g

In the above question find the acceleration of both the block when i F 18 N ii F 36 N

Assertion A man in a closed cabin falling freely does not experience gravity Reason Inertial and gravitational mass have AIIMS 2006 equivalence 1 A 4 D 2 B 3 C

A string tied on a roof can bear a maximum tension of 50 kg wt The minimum acceleration that can be acquired by a man of 98 kg to descend will be Take g 9 8 m s 1 9 8 m s 3 4 8 m s 2 4 9 m s 4 5 m s

In the figure shown all the surfaces are rough Both the blocks have the same mass The friction coefficient between all the surfaces is the same Choose the correct statement ung Br uzung F 15 L A If friction between A and B is kinetic friction between A and ground is also kineti BYIf friction between A and B is Static friction between A and ground is also Static Cff friction between A and B is kinetic friction between A and ground is static D If friction between A and B is static friction between A and ground is kinetic A m wys gmmmmmmm 1 10

59 A point object is moving uniformly towards the pole of a concave mirror of focal length 25cm along its axis as shown below The speed of the object is 1 ms At t 0 the distance of the object from the mirror is 50cm The average velocity of the image formed by the mirror between time t 0 and t 0 25 s is 2019 A 40 cm s B 20 cm s C zero D Infinity ns D At t 0 u 50 cm u 2f at C v 50 cm At t 0 25 s u 25cm f V 0 S t 8 0 25 f 25 cm s vt 0 25 m 25 cm 8 t 0 V 1ms 10 ING 50cm a oduce a minimum deviation of 44 when the angle of incide

29 Figure shows a block of mass 2m sliding on a block of mass m Find the acceleration of each block All surface are smooth 40 1 m s 3 3 5 m s 2m 0 30 m 2 4 20 w 10 erit biori of bobsen T noiena m s m s

Find tensions in strings for given fig A T 2mg T mg BT 2mg 3 T mg 3 C T mg 3 T 2mg 3 DT mg 2 T mg 2 C M L 2

the given arrangement all surfaces are smooth What acceleration should be given to the system for which the ock m doesn t slide down m g m g m M 2 m m g m m g

A block of mass 1 kg is placed on a rough horizontal surface connected by a light string passing over two smooth pulleys as shown Another block of mass 1 kg is connected to the other end of the string The acceleration of the system is coefficient of friction 0 2 A 0 8 g B 0 4 g 1kg 1kg C 0 5 g D zero

inclined plane of length 3 m The first 1 m of the plane is smooth and the next 2 m is rough The block is released from rest and again comes to rest at the bottom of the plane If the plane is inclined at 30 with the horizontal find the coefficient of friction on the rough portion a C 2 3 4 Rough R 30 Smooth 2 m Q Fig 8 272 1 m b P d 2 3 5

9 A small bead of mass 1 g is placed bottom of a watch glass of radius R 1 m It rouot of ebamei sobrino is displaced by h 1 cm along the glass noitont yd 29 stor bus surface and released Find the total distance sulnave sease oniqgil2 described by it before it comes to rest if the oggo ni stato anebrilyo coefficient of friction between bead and watch abega isen Instanco glass is 0 2 ebnilyo llamarlt toytingla h A 5 cm C 15 cm B 10 cm tal w D 20 cm 8 SA1 8 L2 if

1 A particle is acted upon by the forces of magnitudes 5 N 4 N and 3 N respectively in directions east north and west Draw vector diagram to obtain the magnitude of resultant force and draw direction of this force in diagram

kg mass is holding a light rope that passes over a frictionless pulley A bunch of bananas of the same mass 20 kg is tied to the other end of the rope In order to get access to the bananas the monkey starts climbing the rope The distance between the monkey and the bananas 1 Decreases 2 Increases 3 remains unchanged

m Two balls of mass m and hang at the two ends of a string that 10 passes through a fixed tube and one of the balls lies in the tube while the other is outside of the tube The mass m 10 is rotating about PQ A 53 C 60 1 B 30 D 37 m P 37 0 as shown in figure Coefficient of friction between the tube and the ball is 1 Ball which is inside the tube remains in rest and the time period of revolution of the smaller ball is maximum Find the angle 0 which is made by the string with vertical PQ m 10

A block of mass 1 kg is at rest relative to a smooth wedge moving leftwards with constant acceleration a 5m s Let N be the normal reaction between the block and the wedge Then g 10m s zong essi AYN 5 5 N B N 15 N a 0 jug 1 tane N ungcs37 2 20x40x 160 D tan0 2 I 8 0 6716 In

EXAMPLE 11 Feeling Weightlessness A man of mass 70 kg stands on a weighing scale in a lift which is moving i upwards with uniform speed of 10 m s ii downwards with a uniform acceleration of 5 m s iii upwards with uniform acceleration of 5 m s What would be the readings on the scale in each case iv What would be the reading if the lift mechanism failed NCERT and it hurtled down freely under gravity

In the situation given all surfaces are frictionless pulley is ideal and string is light If F Mg 2 find the acceleration of both the blocks in vector form A acceleration of block 2 is zero B acceleration of block 1 is 1 4 2 C acceleration of block 1 relative to block 2 is 19 0 g D acceleration of block 2 relative to block 1 is 2 772 M M F L y

of 15 A ball of mass 1 kg is dropped from 20 m height on ground and it rebounds 5 m Find magnitude of change in momentum during its collision with the Take g 10 m s

As shown in figure pulley is ideal and strings are massless If mass m of hanging block is the minimum mass to set the equilibrium of system then A m 2 5 kg B m 5 kg C force applied by 20 kg block on inclined plane is 179 N D force applied by 20 kg block on inclined plane is 223 N 4 Tem 20kg 0 37 0 37 H 0 5 NA m

3 A balloon with mass m is descending down with an acceleration a where a g How much mass should be removed from it so that it starts moving up with an acceleration a 2ma a b g a ma g a c 2ma g a ma d 2014

For the arrangement shown in the fig below the tension in the string m 1 kg is Given tan 0 8 39 1 6N 3 0 4 N 2 6 4N 4 zero 0 8 27 89

A long plank P of mass 5 kg is placed on a smooth floor On P is placed a block Q of mass 2 kg The coefficient of friction between P and Q is 0 5 A horizontal force of 15N is applied to Q as shown in figure and you may take g as 10 N kg Now A the reaction force on Q due to P is 10N B the acceleration of Q relative to P is 2 5 m s C the acceleration of P relative to the floor is 2 0 m s D the acceleration of centre of mass of P Q system relative to the floor is 15 7 O

If the surface temperature of the sun and its mass were to remain constant and its radius were to increase by a factor of 2 the equilibrium temperature of a planet Tp would B increases by a factor of 2 D increase by a factor of 4 A decreases by a factor of 2 C increase by a factor of 23 2

If a boat can have a speed of 4 km hr in still water for what values of speed of river flow it be managed to row boat right across the river without any drift A 4 km hr C only 4 km hr B greater than zero but less than 4 km hr D none of these

A block of metal weighing 25 kg rests on a horizontal surface the coefficient of static friction between the metal and the surface being 0 3 Find a the horizontal force needed just to pull block b the force applied at an angle of 30 that will just pull the block 75 5 N 72 32 N

A body is moving along the ve x axis with uniform acceleration of 4ms2 Its velocity at x 0 is 10ms The time taken by the body to reach a point at x 12m is 2s 3s 2 3s 4s 3 4s 8s 4 1s 2s

A lift is moving downwards with an acceleration equal to acceleration due to gravity A body of mass m kept on the floor of the lift is pulled horizontally If the coefficient of friction is u then the frictional resistance offered by the body is DPMT 2004 a mg c 2 mg b mg d Zero

A book of mass 5 kg is placed on a table and it is pressed by 10 N force then normal force exerted by the table on the book is 1 10 N 3 59 N 2 4 70 N 50 N