Newton's law of motion Questions and Answers

On a large slippery ground a boy left his dog sitting and walks away with a constant velocity Ub 2 0 m s When he is xo 199 m away from the dog the dog decides to catch him and thereafter move together The dog cannot develop acceleration more than a 2 0 m s in any direction In what minimum time will the dog meet the boy

A block is placed on an inclined plane moving towards right horizontally with an acceleration aog The length of the plane AC 1 m Friction is absent everywhere Find the time taken in seconds by the block to reach from C to A dong A B 37

In the system shown wedge of mass 5 M The pulleys are ideal and the cords are there is friction inextensible anywhere M 5M 2M A initial acceleration of wedge is C tension in string is B initial acceleration of wedge is D tension in string is no 14 mg 25 17 mg 25 3g 25 2g 25

3 A uniform rope of length 10 cm and mass 15 kg hangs vertically from a rigid support A block of mass 5kg is attached to the free end of the rope A transverse pulse of wavelength 0 08 m is produced at the lower end of the rope The wavelength of the pulse when it reaches the top of the rope will be a 0 08 m c 0 16 m b 0 04 m d 0 m 15 kg 5kg

3 14 Give examples of a one dimensional motion where a the particle moving along positive x direction comes to rest periodically and moves forward b the particle moving along positive x direction comes to rest periodically and moves backward

Paragraph for Questions 9 and 10 For the given system of blocks and a concave mirror answer the following Assuming A B C are very small Focal length of mirror is 20 cm y A Cure B Mark the CORRECT statement s A Speed of A is 8 m s when C is moving down with speed 8 m s B Speed of B is 8 m s when C is moving down with 8 m s C Speed of A is 12 m s when C is moving down with 8 m s D Speed of A is 12 m s when C is moving down with 12 m s 0 Mark the CORRECT statement s C X A When A is at x 30 cm image is at x 60 cm B When A is at x 30 cm image is at x 60cm C When C moves with a speed 8 m s downwards image of A moves with a speed 12 m s D When C moves with a speed 8 m s downwards image of A moves with a speed 48 m s

A dynamometer D which is a device used to measure force is attached to two blocks of masses 6 kg and 4 kg Forces of 20 N and 10 N are applied on the blocks as shown in the figure The reading of the dynamometer is 6 kg D 4 kg

Q6 For the bar shown in figure 4 calculate the reaction produced by the lower support on the bar Take E 200 GN m2 Find also the stress in the bars 1 2m m N 55 KN R A 110 mm A 220 mm 1 2m Figure 4 30 cm B 30 KN 20 KN 20 cm Figure 5 10 cm D 15 KN

A ball of mass 1 kg dropped from 9 8 m height strikes the ground and rebounds to a height of 4 9 m If the time of contact between ball and ground is 0 1 s then find impulse and average force acting on ball COLLOXWIN PA

kept horizontally One end of the plank is now lifted so that it gets tilted making an angle 0 from the horizontal as shown in the figure below The maximum value of 0 so that the football does not start rolling down the plank satisfies the figure is schematic and not drawn to scale Plank a sin 8 r R b tan 8 r R c sin r 2R 2r R 0

with a light string which passes over a massless pulley as shown in figure The magnitude of acceleration of centre of mass of both the blocks is neglect friction everywhere A 3 1 Correct Answer B 3 1 g 802 60 D 3 1

31 A uniform rope having mass m hangs vertically from a rigid support A transverse wave pulse is produced at the lower end The speed u of wave pulse varies with height h from the lower end as a c h h b d h h

A man is dragging a trunk up the loading ramp of a mover has a slope angle of 20 0 and the man pulls upward with direction makes an angle of 29 5 with the ramp 20 0 a How large a force is necessary for the componen ramp to be 52 0 N

YOU DIDN T ATTEMPT ABCD is a rectangle forces of 9N 8N 3N act along the lines DC CB and BA respectively in the directions indicated by the order of the letters Then the resultant force is 9N D A 8 N 5 N 20 N 3N C 8N B

Determine the magnitude and direction of the friction force acting on the 100 kg block shown if first a 30 and second a 10 The coefficient of static friction is 0 20 and the coefficient of kinetic friction is 0 17 The forces are applied with the block initially at rest 1 Section A Take P 400 N 2 Section B Take P 250 N P 100 kg

4 40 A wire of mass 100g is carrying a current of 2A towards increasing x in the form of y x 2m x 2m This wire is placed in a magnetic field B 0 02 k T The acceleration of the wire is A 1 6 m s 1 6 m s B 3 2 m s D Zero

A block of mass 2 kg released from smooth fixed wedge inside the elevator which is moving downward with an acceleration a 5 m s shown in the figure The value of acceleration of b w r t wedge will be g 10 m s 30 10 m s 5 m s 2 5 m s 5 2 m s

d all of these 7 Three concurrent co planar forces 1 N 2 N and 3 N acting along different directions on a body a can keep the body in equilibrium if 2 N and 3 N act at right angle b can keep the body in equilibrium if 1 N and 2 N act at right angle c cannot keep the body in equilibrium d can keep the body in equilibrium if 1 N and 3 N act at an acute angle

Two blocks of mass m and m are connected with a massless string These blocks are placed over a smooth surface of inclined plane at an angle of 30 A force of 50 N is applied to pull these blocks as shown in Figure Calculate the acceleration of the blocks Given m 0 1 kg and m 0 2 kg m 30 m T

a maximum tension of 900 N The case in which the rope will break if the monkey Climbs up with an acceleration of 7 m s Climbs down with acceleration of 6 m s Climbs up with uniform speed of 5 m s Falls down the rope nearly freely under gravity

A body of mass 5 kg is pulled by a force F 41 31 N from rest on a smooth horizontal table in x z plane The time at which it will attain a speed of 4 m s is 1 3 s 15 s 4 s 4 3 25 s

The 9 kg block is moving to the right with a velocity of 0 6 m s on a horizontal surface when a force F whose time variation is shown in the graph is applied to it at time t 0 Calculate the velocity v of the block when t 0 4s The coefficient of kinetic fricton is k 0 3 This question includes concepts from Work Energy Power chapter F N 36 F in N 1 0 6 m s 2 1 2 m s 3 1 8 m s 4 2 4 m s 0 2 t in sec 0 4 9 kg H 0 3 v 0 6m s

45 F S W F East a not accelerate If three forces of same magnitudes are applie on block as shown block may b accelerate along N E W c accelerate along S W S

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

opped ng inclined plane If bounces hits the plane again bounces and so on let us Label the distance between the point of the first and second hit d12 and the distance between the points of second and the third hit is d23 find the ratio of d12 d23 d 2 d23

13 A uniformly moving cricket ball is turned back by hitting it with a bat for a very short time interval Show the variation of its acceleration with time Take acceleration in the backward direction as positive

Blocks are in contact on a friction less table A horizontal force F 3N is applied to one block as shown The force exerted by the smaller block m2 on block m is A FL 1N B 2N c 3N m 2kg m 1kg

A uniform rope of mass 2 kg and length 1 m is placed on smooth horizontal surface A horizontal force 4 Ni applied at its one end as shown in figure The tension at mid point of the rope will be 1 m 1 N 4 N 2 N 3 N 4 N

A loaded ore car has a mass of 950 kg and rolls on rails with negligible friction It starts from rest and is pulled up a mine shaft by a cable connected to a winch The shaft is inclined at 30 5 above the horizontal The car accelerates uniformly to a speed of 2 35 m s in 15 0 s and then continues at constant speed a What power must the winch motor provide when the car is moving at constant speed kW b What maximum power must the motor provide kW c What total energy transfers out of the motor by work by the time the car moves off the end of the track which is of length 1 250 m

Two masses of 2 kg and 3 kg are connected by an ideal string which is passing over an ideal pulley as shown in figure If system is released from rest then tension in the string which is connected two masses is g 10 m s 2 kg 3 kg 24 N 10 N 20 N 30 N

A block of mass 1 kg is placed on the another block of mass 2 kg which is placed on ground as shown in figure The normal force on the 2 kg block by the ground will be g 10 m s 1 kg 2 kg 10 N 20 N 30 N 50 N

The collar A is free to slide along the smooth rod B mounted in the frame The plane of the frame is vertical The horizontal acceleration a of the frame necessary to maintain the collar in a fixed position on the shaft is ms 1 3 00 1 6 0 2 3 B 30 2 4 a 3g g 5

Apparent weight of a person in an elevator is more than actual weight if elevator is Going up and slowing down Going up and speeding up Going down with constant speed Going down and speeding up

7 87 A jet of water issues vertically at a speed of 30 feet per second from a nozzle of 0 1 square inch cross section A ball weighing one pound is balanced in the air by impact of water on its underside Find the height of the ball above the level of jet Take g 3 ft s Ans 4 6 feet

The greatest and the least resultant of two forces acting at a point is 10N and 6N respectively If each forces is increased by 3N find the resultant of new forces when acting at a point at an angle of 90 with each other sig mot 1 146N 2 124 N 3 188 N 4 114 N

An inclined plane of inclination 45 is placed in uniform horizontal electric field of 100 N C as shown in figure A block of mass 1 kg having charge q is sliding down on the plane with constant velocity If coefficient of friction is 0 5 then the value of charge q is g 10 m s2 25 1 5 x 10 2 C 2 1 x 10 C 3 3 3 x 10 C

4 24 What is the conservation of string All of the accelerations are defined to be positive upward relation for the Atwood s machine shown in Fig 4 13 a a az b a a3 c a2 a a3 2 d a2 a a3 e a 2 a az Figure 4 13

H Figure shows a uniform disc with mass M 2 4 kg and radius R 20 cm mounted on a fixed horizontal axle A block of mass M 1 2 kg hangs from a massless cord which is wrapped around the rim of the disc The tension in the cord is A 12 N C 24 N B 20 N D 6 N Point WING 70 Apr220cm M 2 4 Ky m 21 2 kg

Below the fixed end of the insulating horizontal thread there is a fixed charge A of 20 C which is same as the charge of the small body B of mass m at the end of the thread as shown in the figure The body B is released and when it is at the lowest position the thread is vertical Assume that thread does not strike the fixed charge The body B comes to a stop at the lowest position 3 m 4 m m do What is the initial acceleration of the small body A 8 8 m s C 9 5 m s B 10 5 m s D None of these

A block projected from the bottom of an inclined plane stops after 0 5 s after travelling a certain distance along the inclined plane The velocity of projection is 5 m s The angle of inclination of the inclined plane is 30 The coefficient of friction is Take g 10ms A A B C 1 2 3 14

In the arrangement shown in the figure friction exists only between the two blocks A and B The coefficient of static friction 0 6 and coefficient of kinetic friction 0 4 the masses of the blocks A and B are m 20 kg and m 30 kg respectively Find the acceleration in s of m if a force F 150N is applied as shown in the figure Assume that string and pulleys are massless M m m F 150N 60

A mass m is suspended from the two coupled springs connected in series The force constant for springs are K and K The time period of the suspended mass will be wwwwwwwww K 00000 00000 K T 2 T 2T T 2T T 2 m K K m K K m K K K K mK K K K

A bob is hanging over a pulley inside a car through a string The second end of the string is 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 equal to car

A force F 3x 3 is acted upon a pa Choose the correct option 1 Particle will not perform SHM 2 Particle will perform SHM about x 3 3 Particle will perform SHM about x 1 4 Particle will perform SHM about x 1

A plank of mass M 8 kg with a bar o mass M 2 kg placed on its rough surface lie on a smooth floor of elevator ascending with an acceleration g 4 The coefficient of friction is u 1 5 between m and m A horizontal force F 30 N is applied to the plank Then the acceleration of bar and the plank in the reference frame of elevator are

The system in figure is given an acceleration Weight of the ball is W a The force on the ball from vertical surface is 1 15 W The force on the ball from inclined surface is b 30 w 0 58 c The force on the ball from vertical surface is W 0 58 8

Paragraph for 17 to 18 A block of mass M rests on a smooth horizontal surface over which it can move without friction A sma body with mass m lies on the block as shown in the figure The coefficient of friction between the body an the block is u M m B For how many of the following different values of force F mass m slides over the block i M m g ii 2 M m g iii 3 M m g iv 4 M m g A One B Two F m C Three If the force F is sufficient enough for the sliding to begin in what time t will the mass m fall off M 2ML 2ML 4ML 4ML A D F u M m g VF 2 M m g VF M m g VF 2 M m g C D All four

and acts up the plane if body has tendency to slide down lustration 43 v A block of mass 1kg lies on a horizontal surface of a truck the coefficient of static friction between the block and the surface is 0 6 What is the force of friction on the block if the acceleration of the truck is 5 m s Solution mg

2 8 A 4 kg block rests on top of a 5 kg block which rests on a frictionless table The coefficient of friction between the two blocks is such that the blocks start to slip when the horizontal force F applied to the lower block is 27 N Suppose that a horizontal force is now applied only to the upper block What is its maximum value for the blocks to slide without slipping relative to each other

All pulleys and threads are ideal C is a point on the thread as shown When the system is released from rest at that instant 5g A Acceleration of point C is upwards 2 B Acceleration of block B is 2g upwards C Acceleration of block A is g downwards D Acceleration of point C is g downwards B 777777 m A accelarati due to gravity is M