Newton's law of motion Questions and Answers

17 A block is placed on an inclined plane moving towards right horizontally with an acceleration a g The length of the plane AC 1 m Friction is absent everywhere The time taken by the block to reach from C to A is g 10 m s A a 126 ao g B 10740 30 0 95C

20 A triangular wedge is placed on smooth horizontal surface A block is placed on wedge as shown in the figure Coefficient of friction between block and wedge is u Initially system is at rest Find minimum value of u so that system remains at rest a tane b cos 0 m M c 1 ton0 d sine

A single plate clutch effective on both sides has a mean diameter of 150mm The axial load on the clutch plate amounts to 1000N uniformly Taking friction coefficient equal to 0 33 Calculate the torque transmitting capacity of the clutch use uniform wear theory O 25N m O 33 5N m 0 25 10 EN m

11 In the arrangement shown in figure coefficient of F 20N friction between the two blocks is 1 2 The force of friction acting between the two blocks is a 8 N c 6 N b 10 N d 4 N 2kg 4kg F 2N

a 2 m s b 4 m c 6 m s 9 A car is going at a speed of 6 m s when it encounters a 15 m slope of angle 30 The friction coefficient between the road and tyre is 0 5 The driver applies the brakes The minimum speed of car with which it can reach the bottom is g 10 m s a 4 m s c 7 49 m s 30 b 3 m s d 8 45 m s

7 A person applies a constant force F on a particle of mass m and finds that the particle moves in a circle of radius r with a uniform speed v as seen from an inertial frame of reference a This is not possible b There are other forces on the particle c The resultant of the other forces is mu r 2 towards the centre d The resultant of the other forces varies in magnitude as well as in direction

Q14 A smooth inclined plane having inclination with the horizontal is inside a lift which is moving down with a retardation a The time taken by a body to slide down the inclined plane from rest will be a b c d 2L g a sine 2L g a sine 24 asing 21 gsing

a long rough plank B of same mass as shown in figure The plank is placed over a smooth a horizontal surface At time t 0 block A is given a velocity vo in horizontal direction Let v and v be the velocities of A and B at time t Then choose the correct graph between v or v and t V1 U2 V Or V c V1 V2 V2 V Or V2 V 2 b BA B d V or V V V2 V or V V2 Vo V1

8 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 40N only The maximum acceleration in upward direction with which the monkey can climb safely is Neglect friction and take g 10 m s 30 2 h 4 m a 0 6 m s2 d 8 m s

71 A body of mass M rests on a horizontal plane having coefficient of friction u At t 0 a horizontal force is applied that varies with time F t Fot where F is a constant vector The time instant to at which motion starts and distance moved in t seconds will be Fo Mg Mg 1 F and t to b and 6 M M Fo Fo Fo t to d and Mg M a Fo 0 Fo c and Mg 2 Mg t to t t 0 0

6 A wedge of mass 2m and a cube of mass m are shown in figure Between cube and wedge there is friction The minimum coefficient of friction between wedge and ground so that wedge does not move is a 0 10 no b 0 20 c 0 25 0 45 d 0 50 2m

A heavy flexible inelastic chain of length and uniform linear mass density u and length L is placed almost symmetrical on a light pulley which can rotate shaft about its centre O as shown 31 R B 0 15L X When the system is released the chain descends from right side due to slight unsymmetry The height climbed by A before chain looses contact with the pulley will be R may be taken to be small in this part 0 0351

Consider the Atwood system shown below The pulleys are ideal the ropes are light and the inclines have negligible friction The spring has a stiffness of 50 N m and when the system is released from rest is initially stretched by 0 4 m Mass A is 9 1 kg and mass B is 45 0 kg No the incline angles are such that cos 0 12 13 sin 0 5 13 for the left incline and cos OR 3 5 sin OR 4 5 for the right incline A Take g 10 0 m s When block B slides 2 4 m down the incline determine a 2 the exact integer change in block A s gravitational potential energy b 2 the exact integer change in block B s gravitational potential energy c 2 the exact integer change the system s spring potential energy d 2 the speed of block A accurate to three sig digs m s fixed G B

The total mass of cart is 2 metric ton in which 1 metric ton sand is loaded System is initially at rest The sand leaks out of the cart from the hole at Bottom at the rate of 0 5 kg s and an external horizontal force of 10N is acting on it The final velocity of cart when the sand completely leaks out is 3 1 13 86 m s 3 20 08 m s 2 14 26 m s 4 16 39 m s

E Physics A rod of mass 2m moves vertically downward on the surface of wedge of mass m velocity of rod if the velocity of wedge is 1 m s 0 45 2m

vertically upward The acceleration of centre of mass is A particle of mass m is thrown horizontally from the top of a tower and another particle of mass 2m is thrown 1 g 2g and Rotational Motion 9g 3 g 4

A truck of mass 500 kg moving with constant speed 10 m s If sand is dropped into the truck at the constant rate 10 kg min the force required to maintain the motion with constant velocity is 5 1 N 5 N 2 3 N 4 3 2 N

c 100 m s d 293 A conveyor belt is moving horizontally at a speed of 4 m s A box of mass 20 kg is gently laid on it It takes 0 1 s for the box to come to rest If the belt continues to move uniformly then the distance moved by the box on the conveyor belt is AMU Medical 2007 a zero c 0 4 m b 0 2 m d 0 8 m

A U tube with both ends open to the atmosphere is partially filled with water Oil which is immiscible with water is poured into one side until it stands at a distance of 10 mm above the water level on the other side Meanwhile the water rises by 65 mm from its original level see diagram The density of the oil is NEET 2017 Pa A Oil B 65 mm 65 mm 1 650 kg m 3 2 425 kg m 3 3 800 kg m Pa FI E 110 mm Final water level Initial water level Water

1 Consider the following two equations 1 A R mi ri and B a CM In a noninertial frame a both are correct c A is correct but B is wrong M b both are wron

The Omani Noor Majan car is of mass M kg is going up Jabal Akhdar at angle 0 with N people inside the car each of mp kg The car model provides L Newtons of lift and it is accelerating up at a m s2 The road provides a coefficienct of kinetic friction uk What is the force exerted by the engine Hint This question has no numbers Your answer needs to be an equation Submission status

D A uniform sphere is placed on a smooth horizontal surface and a horizontal force F is applied on it at a distance h above the surface The acceleration of the centre a is maximum when h 0 b is maximum when h R c is maximum when h 2R d is independent of h

Equal force F mg is applied to string in all the three cases Starting from rest the point of application of orce moves a distance of 2 m down all cases In which case the block has maximum kinetic energy 1 m C 3 m D equal in all 3 cases

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 What is the acceleration with which the system is moving Take g 10 ms 1 Zero 1kg 2 2 ms 2 T 6kg T 2 3 4 ms 3kg 4 3 ms2

horizontal A heavy uniform chain lies on a table top If If the coefficient of friction between the chain and the table surface is 0 25 then the maximum fraction of the length of the chain that can hang over one edge of the table is A 20 25 35 O 15 40

2 Two cars having masses m and m move in circles of radii r and r respectively If they complete the circle in equal time the ratio of their angular speeds o 00 is a m m b r r c m r m r d 1

1 Figure 6 E12 shows a small block of mass m kept at the left end of a larger block of mass M and length 1 The system can slide on a horizontal road The system is started towards right with an initial velocity u The friction coefficient between the road and the bigger block is u and that between the block is u 2 Find the time elapsed before the smaller blocks separates from the bigger block E M

Leeeee 0 M A block of mass m is on a rough horizontal surface and is attached to a spring with spring constant k The coefficient of kinetic friction between the surface and the block is When the block is at position x 0 the spring is at its unstretched length The block is pulled to position x as shown above and released from rest The block then travels to the left and passes through x 0 before coming momentarily to rest at position x x x 2 15 Which of the following is a correct expression for the kinetic energy of the block as it first travels through position 1 0 B x 2 C k 2 mgxo D kx 2 3 mgx 2 E kx 2 2 mgx the coefficient of kinetic friction A B C D kxo 4mg kxa 2mg 3kxo 4mg kxo mg 2k mg 17 Which of the following is a differential equation that could be used to solve for the block s position x as a function of times when it is moving to the left A m B m4 x C m sive D m E m kx mg kx mg kx mg Ax

The tension in the string as shown in the figure is g 10 m s All surfaces are smooth 10 kg 37 OPTIONS CLEAR RESPONSE OA 23 3 N OB 50 N 5 kg OC 30 N MARK FOR REVIEW

Consider a frame that is made up of two thin 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 A 145 70 B 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

What force should be applied on the wedge so that block over it does not move All surfaces are smooth m 1 F M m g cot 0 3 F M m g sin 0 M 2 4 F F M m g tan 0 F M m g cos 0

An electric fan is placed on a stationary boat and air is blown with it on the sail of the boat Which of the following statements is correct 1 The boat will be uniformly accelerated in the direction of the flow of the air 2 The boat will start moving with uniform speed 3 The boat will be uniformly accelerated opposite to the direction of flow of air 4 The boat will remain stationary as before

There is a massless square frame through which four identical massless and inextensible strings are passing The strings are also passing over four pulleys which are fixed with four supports lying in the same horizontal plane symmetrically At a given instant string between pulley and frame is making angle of with the horizontal plane Both the ends of all strings are connected with identical point masses each one having mass of mo The system lies is uniform gravity What is the acceleration of the frame just after release 3 D view Top view

What is the relation between velocities of points A and B in the given figure 1 V 3 V V VB COSO cose V V sin sin 0 A VB A 10 B V 2 V 1 4 Vr 8 0 Vc C V VB COSO cos V VB cose 2 cose VB VB

1 A small block of mass 200 g is kept at the top of a frictionless incline which is 10 m long and 3 2 m high How much work was required a to lift the block from the ground and put it at the top b to slide the block up the incline What will be the speed of the block when it reaches the ground if c it falls off the incline and drops vertically on the ground d it slides down the incline Take g 10 m s

5 An object of mass 100 kg is initially at rest on a horizontal frictionless surface At time t 0 a horizontal force of 10 N is applied to the object for 1 s and then removed Which of the following is true of the object at time 1 2 s if it is still on the surface A It is at the same position it had at t 0 since a force of 10 N is not large enough to move such a massive object B It is moving with constant nonzero acceleration C It is moving with decreasing acceleration D It is moving at a constant speed E It has come to rest some distance away from the position it had at t 0

experiences a net force given by the function F 31 At time 0 the car has a velocity of 4 m s in the positive direction and is located 8 m from the origin 16 The car will come instantaneously to rest at time equal to A 17 Which of the following best shows a graph of position d versus time for the car d se by dabad HR ail com Seger 10 SAT AP her TAS ExclusiveSAT com 9 D

2 If the tension in the string in figure 6 E3 is 16 N am the acceleration of each block is 0 5 m s find the frictio coefficients at the two contacts with the blocks 2 kg 41 42 4 kg 30

HT A small block of mass m is placed inside a smooth hollow sphere of radius R at lowest position Initially system was at rest as shown in the figure Now the sphere is given a constant horizontal acceleration g by an external agent The maximum angular displacement of block with vertical w r t sphere is 1 60 3 45 vilsom no biser VIII de mu He 201 2 30 4 90 lon N

37 A bullet of mass 10 g strikes a fixed target and penetrates 8 cm into it before coming to rest If the average force of resistance offered by the target is 100 N with what velocity does it strike a 10 m s b 20 m s c 30 m s d 40 m s

Two identical rollers each of weight Q 100N are supported by an inclined plane and a vertical wall as assuming smooth surfaces find the reaction induced at the point of support A B and C shown in Fig HIGHLY COM TI 16 DO

The electric field is 200 V m at a distance of 30 cm from the centre of a dielectric sphere of radius 10 cm Then E at 5 cm distance from the centre of sphere is 1 100 V m 3 1800 V m 2 900 V m 4 zero

W A w W C 3W C As shown in the figure a square uniform lamina of weight W is hinged to a vertical wall at A with its plane vertical Another body of weight Wis saspended from the opposite corner C The lamina is supported with its diagonal AC horizontal by means of a horizontal string joining B to the wall The tension T in the string is B 2W D 4W

ass 2 kg released top smooth fixed wedge inside the elevator which is moving downward with an acceleration a 5 m s as shown in the figure The value of acceleration of block 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 a

23 A wedge of height h is released from rest with a particle P placed on it as shown The wedge slides down an inclined which makes an angle 8 with the horizontal All surfaces are frictionless P will reach the surface of the inclined in time A 2h gsin 0 B 2h gsin 0 cos 0 C 2h g tan 0 D 2h gcos 0

11 3 0 4 ft sec 4 0 8 ft sec A body of mass 2 kg is kept on a rough horizontal surface as shown in the figure Find the work done by frictional force in the time interval t 0 tot 5 sec 10 N 1 zero 3 20 J 2 kg 30 10 N m H 0 5 2 15 J 4 data insufficient

B are attached to separate nails A and B in the same level so that the core assume shape of a catenary In which case is the cord stretched longer 3 A uniform rope of length 12 m is suspended between two fixed nail A and B that are in the same horizontal level If the rope makes an angl 8 sin 0 6 with the horizontal at the nails find depth h of the lowes point on the rope below the nails and radius of curvature p of the rop at the lowest point

Lifting of a Conical Vessel A conical vessel without a bottom stands on a smooth table A liquid is poured in the vessel and as soon as liquid level rises to h the vessel is lifted up at the bottom by liquid pressure The base radius of vessel is R and its weight is W Find the density of liquid Normal reaction of botton dueti li hang

A particle of mass m is moving along the side of a square of side a with a uniform speed v in the x y plane as shown in the figure Which of the following statements is false for the angular momentum Labout the origin R 1 mv ak when the particle is moving from C to D 2 R 2 L mv ak when the particle is moving from B to C 2 3 mv RK when the particle is moving from D to A 2 mv 4 L RK when the particle is moving from A to B avv A 45 R D Aa va B 201

C Three identical cars A B and C are moving at the same speed on three bridges The car A goes on a plane bridge B on a bridge convex upwards and C goes on a bridge concave upwards Let F FB and Fo be the normal forces exerted by the cars on the bridges when they are at the middle of the bridges Then 1 F is maximum of the three forces 2 FB is maximum of the three forces 3 F is maximum of the three forces C