Newton's law of motion Questions and Answers

4 A block of mass m slides on a frictionless inclined planc which is driven so that it moves horizontally the displacement of the plane at time t being some known function r t Obtain the equation of motion

A weight of hundred newton is suspend ed by two wires made of steel and cop per as shown in figure length of Steel w ire is 1 metre and copper wire is root 3 metre find the ratio of change in length of copper wire to change in length of St eel wire during smallest why steel is eq ual to 2 into 10 to the power 11 Newton per metre square why copper is equal t o 1 into 10 to the power Newton per me tre square

The uniform square plate square plate of mass 6 kg is placed on the x y plane If a horizontal force P 12 N is applied to one corner in the direction shown Initial acceleration of point A is a 3 m s Find the value of B 2 B is smallest integer A 45

In the figure below pulleys and strings are ideal coefficient of friction between block and surface is 0 2 Find acn a of hanging block Both blocks have same mass m 2 kg A 2 4 m s B 3 6 m s m 0 2 al wwwww m C 0 8 m s D 1 2 m s

57 An elevator car whose floor to ceiling distance is equal to 3 8m starts ascending with constant acceleration of 2 2 m s 4 second after the start a bolt begins falling from the ceiling of the car The free fall time of the bolt is a 0 132 second b 0 931 second c 1 second d 0 633 second

Question No 13 Stum Chem Getint A Ply Sachin D Chem Section Maths Section Phy Section A This section contains 20 SINGLE CORRECT TYPE questions Each question has 4 choices 1 2 3 and 4 out of which only one is correct In the arrangement shown the siring does not sip over putey Consider puley as a solid cyinder of mass 4m and radius R The acceleration of block Ais View in a

2 A cylindrical helium balloon of volume 1 m and length 1m is tied to a massless string which in turn is tied to the floor of the cart initially at rest The cart starts moving horizontally with an acceleration of 10 m s If the cart is filled with air of density 1 2 kg m the density of helium is 0 2 kg m and the balloon material has negligible mass then find a The tension in the string before the cart starts to move b In which direction will the balloon move just as the cart starts accelerating 10N loft b10N right 10 loft d 10 EN right

A ball is projected upwards from the top of a tower with a velocity of 50 ms making an angle of 30 with the horizontal The height of the tower is 70 m After how many seconds from the instant of throwing will the ball reach the ground 1 2 s 2 5 s 3 7 s 4 9 s

Consider the satellite that is shown in the below figure mass of 3500 kg is in a circular orbit around a planet The satellite travels with a constant speed of 8560 m s The radius of the circular orbit is 2 50 x 104 m satellite At the instant shown in the figure which arrow indicates the direction of the net force on the satellite a planet Select one O a b O b a O c d O d e b d

Two bodies of equal masses are connected by a light inextensible string passing over a smooth frictionless pulley The amount of mass that should be transferred from one to another so that both the masses move 50 m in 5 s is a 30 b 40 c 70 d 50

8 Two wooden blocks are moving on a smooth horizontal surface such that the mass m remains stationary with respect to the block of mass M as shown in the figure The magnitude of force P is P a gtan c M m cosec M m B b mg cos B d M m a tan

Block A is hanging from a vertical spring and is at rest Block B strikes the block A with velocity v and sticks to it And v is such that it just attends its natural length then choose the correct option s 6 mg k A v 10 m g2 k B v C The energy loss during collision is D The energy loss during collision is 3m g 2K m g 2K J J

A block of mass m is released on a smooth inclined plane of inclination 30 and mass M Height of the block varies with time as h 1 5 1 5 t h in metre t time in second What is the acceleration of M A 1 m s 2 B 3 m s 30 M h C 3m s D 2 m s

Q 9 A bar 2 m long a negligible weight rests in horizontal position on two smooth inclined Determine the distance x at which the load Q 100 N should be placed from point B to keep t horizontal P 200N k 0 5m 30 2m Q 100N xx B 45

Two masses M M2 are placed in contact with each other on a frictionless table A force F is applied as in fig a Let F denotes the force on My due to M i 11 A force of the same magnitude F is applied as in fig b Let F denotes the force on My due to M The ratio F Fis Options 1 2 3 M M M M M M fig a M M M M fig b

Rain is falling with a speed of 4m s is a direction making an angle of 30 with vertical towards south What should be the magnitude and direction of velocity of cyclist to hold his umbrella exactly vertical so that rain does not wet him 1 2m s towards north 2 4m s towards south 1635 2m s towards south A Amla tou

A rocket starts from rest and accelerates with g When speed becomes Vo the engine is switched off What is the average speed from ground till it reaches a stop g acceleration due to gravity Options 1 2 3 V 2 2 V 2 2 Vo 3

A ball of mass 2 kg falling vertically downwards strikes the ground with a speed 10 m s If coefficient of restitution is e ball is 3 4 40 N S 30 N S 10 N S 20 N S W View In English the impulse given by the ground to the

14 A small body of mass m starts from rest sliding down a rough inclined plane as shown If the angle 8 is varied so that time of sliding will be least Find that minimum time Note the base length of inclined plane remains constant m Fix K 3 0 30 3 m

The resultant of two ropes pulling a cart as shown in Fig 2 38 acts along the axis Som cart and has a magnitude of 6 kN What would be the tension in the ropes when 0 30 Proceed to workout the value of 0 so that the tension in the rope AB is minimum Also find out this minimum tension Bow of llows TAT A 0 35 Resting resent

A block A of mass 2 kg is hanging in a vertical plane with a spring of stiffness constant k 100 N m A block B of mass 1 kg is kept on block A and the system is in equilibrium Suddenly block B is removed The amplitude of resulting SHM of A is

Find the acceleration of rod A and wedge B in the arrangement shown in figure if the mass of rod equal that of the wedge and the friction between all contact surfaces is negligible and rod A is free to move downwards only Take angle of wedge as 37 37 d black C

A load attached to the end of a spring and in equilibrium produces 9 cm extension of spring If the spring is cut into three equal parts and one end of each is fixed at O and other ends are attached to the same load the extension in cm of the combination in equilibrium now is A 1 B 3 C 6 D 9

A projectile can have same range R for two angles of projection It t and t2 are the times of flight in the two cases then what is the product of two times of flight O O O t t R 111 R 1 1 x R

23 24 5 A stone thrown from the top of a building is given an initial velocity of 20 0 m s straight upward Determine the time in seconds at which the stone reaches its maximum height Take g 9 8 m sec a 2 8 1 67 The speed of a projectile when it is at its greatest height is maximum height What is the angle of projection a 60 b 90 c 15 d 45 A man of mass 70 kg stands on a weighing scale in a lift which is moving upwards with a uniform acceleration of 5 ms 2 What would be the reading on the scale 130 kg c 150 kg b 2 04 d 2 7 22 b 120 kg d 105 kg times its speed at half the Section B Attempt any 20 questions If a sphere is rolling the ratio of translational energy to total kinetic energy is given by bis 0 77 0 77 0 77 0 77

surface Two forces F 20 N and F N are acting on A body of mass 2 0 kg is placed on a shooth horizontal the body in directions making angles of 30 and 60 to the surface The reaction of the surface on the body will be F2 Fix a 20 N c 5 N 30 2 kg 60 b 25 N d zero

n the given figure a block A rests on a smooth triangular block B and the block B is given an acceleration of a 2 m s along the plane B normal force on block A due to block B is m g a acceleration of block A relative to block B is a cos 0 If friction is present between block A and B the coefficient of friction should be greater than cos for no relative motion between A and B If friction is present between block A and B the coefficient of friction should be greater than relative motion between A and B a cos g a sin for no

2 62 A box is placed in the middle of the bed of a flatbed truck and is not strapped down The coefficient u between the bed and the box is 0 75 If the truck is travelling at a speed of 22 m s along a horizontal street what is the minimum stopping distance such that the box will not slide 3 Ans 33 ml

9 27 19 I 3 20 T Ga 9 Ra 3kg 2M 27 120 a 139 2 X2 fixed O a 0 Mg T M 2a Mg T aMa Similarly 27 QM a 21 4kg 19 physics Laws of Motion ap a 92 a to 2 T 9 13 N 9 U M a movable Pulley a 0 Las Eve my 20 E Ve 20 ap 9 0 ap 70 2 ap 2a zap 1x 2mg 2 7 4Ma Mg T 2Ma 2019 2 6Ma 29 a 6 a NEE UI

2 52 Two weights W and W are suspended from the ends of a light string passing over a smooth fixed pulley If the pulley is pulled up with acceleration g the tension in the string will be A AW W W W B C W W W W D 2W W2 W W W W 2 2 W W

Two blocks of masses 2 Kg and 3 Kg are placed on a plank An external force of 10N is acting on 2 Kg block and the whole system including the plank is moving vertically up with a constant acceleration ao 2 m s The normal reaction force between the 3 Kg block and Plank is a N Find 10 DIG VO 2 m s asia 13 Kg 2 Kg m 3 Kg 12 Kg HA staan wat te da R 1 10 10 N 2 Kg 3 Kg Plank 120 g 10 m s g 10 m s

0 Three blocks with masses m 2m and 3m are connected by strings as shown in the figure After an upward force F is applied on block m the masses move upward at constant speed v What is the net force on the block of mass 2m g is the acceleration due to gravity a 2mg c 6mg 3m tv b 3mg d Zero

6 Which of the following shows the correct direction of normal reaction R A T C RA w AR W Fext 1 Only A 3 A B D B D R R W W 2 Both A C 4 All of these Fext

2 75 Blocks A and B have masses of 2 kg and 3 kg respectively The ground is smooth P is an external force of 10 N The force exerted by B on A is A 4N B 6N C 8N D 10N P 10 N 2 kg 3 kg B Figure 2 175

MULTIPLE In the arrangement shown in the figure initially the block of mass m is in limiting equilibrium The coefficient of friction between the block of mass m and floor is u Now the particle of mass m is given a horizontal velocity vo The initial distance of the block of mass m from the pulley is The masses of pulley and threads are negligible Choose the correct option s A Acceleration of m just after the velocity given is R Acceleration of m just after the velocity given is m 1 V 1 20 m Song

1 A rope lies on horizontal table so that part of it hangs over the edge The rope begins to slide down when the length of the hanging part is 20 of the entire length The coefficient of static friction between the rope and the table is 1 0 1 2 0 25 3 0 5 4 0 7

A smooth wire is bent into a vertical circle of radius a A bead P can slide smoothly on the wire The circle is rotated about vertical diameter AB as axis with a constant speed as shown in figure The bead P is at rest w r t the wire in the position shown Then is equal to A 2g a C B 3 a D 2 g g A 00

15 Select the correct statement with respect to the given situation M M 1 If M sina M cosa M block M moves upward 2 If M sina M cosa M block M moves downward 3 If M sina M cosa M block M moves downward 4 Both 1 3

Two masses kept on ground are connected by means of a light string that passes over a light pulley as shown Ifm1 2 kg m2 5 kg a vertical force F is applied on the pulley then find the accelerations of both the masses the pulley if a F 35 N b F 70 N c F 140 N

Q As shown in diagram two masses of 3kg and 2kg are suspeded from atwood machine kept inside lift if lift moves up with aceleration of 2m s Find a acceleration of blocks wrt lift b reading of spring balance c acceleration wrt ground 3kg 91743974706 as5716009 gmat og Ta 2m sz ant Sir

Two identical charged balls each of mass m a suspended from a common point The length each string is 1 In equilibrium the distan between balls is r then what will be tensi force in string 1 mgl 1 r 3 mg 2 4 mgl 12 mg 1 r

package of mass 56 kg is pushed up a ramp with a horizontal force of 450 N The leng of the ramp is 3 00 m and the angle between the ramp and the horizontal is 36 If the fin peed of the package is 5 0 m s calculate the initial velocity of the package a 6 7 m s b 8 5 m s c 9 7 m s d 4 5 m s

10 Three equal weights A B and C of mass 2 kg each are hanging on a string passing over a fixed pulley which is frictionless as shown in figure The tension in the string connecting weight B and C is a zero c 3 3 N A B C b 13 N d 19 6 N

A light string fixed at one end to a clamp on ground passes over a fixed pulley and hangs at the other side It makes an angle of 30 with the ground A monkey of mass 5 kg climbs up the rope The clamp can tolerate a vertical force of 40 N only The maximum acceleration in upwards direction with which the monkey can climb safely is Neglect friction and take g 10 m s A 2 m s2 C 6 m s B 4 m s D 8 m s C 11 30 Clamp irs by

In the shown diagram all surfaces are smooth pulleys anc string are ideal Masses of each block is 1 kg If a a are the acceleration of block A and B respectively then choose the correct options g 10 m s m a aB 12 m s 36fm m s aA m s aB 12 m s B ma

a A uniform rope of length L resting on a frictionless horizontal surface is pulled at one end by a force F Derive an expression for the tension in the rope as a function of position along its length b If the rope is pulled vertically upwards by the said force is there any change in the above expression

T 100 N A block of mass 4 kg is pulled with a rope of mass 500 g on a frictionless surface If a force 9 N is applied at free end of the rope force exerted in N by the rope on block would be 8 Rusa Road New Delhi 110005 Ph 011 47623456

2 In figure shown pulleys and string are initially the system is in equilibrium and string connecting m to rigid support below is cut Find the initial acceleration of m in m s lest ellele m m 8 kg m m 2 kg g 9 8 m s

b A 13 50 kg bicycle moving on a smooth surface reaches a speed of 50 m s in 5 s The bicycle starts with a speed of 20 m s i what is the net force acting on the bicycle If 6 N kinetic frictional force is acting in the bicycle calculate the resultant force Assume that the acceleration of the bicycle is reduced to 3 m s 11

A small heavy ball is tied to one end of a string of length L while its other end is fixed If length of the string is L 1 6 m and ball revolves as a conical pendulum as shown in figure then 60 One More Correct Answer s m 2 kg