Newton's law of motion Questions and Answers

A 2 kg block A is attached to one end of a light string that passes over an an ideal pulley and a 1 kg sleeve B slides down the other part of the string with an acceleration of 5 m s with respect to the string Find the acceleration of the block acceleration of sleeve and tension in the string g 10 m s 20 T 5 ar as 5 T 10 arb B 1 1 the as 294 5

Two blocks A and B of masses 10 kg and 5 kg respectively are placed inside a cart which is moving horizontally with an acceleration of 2 m s2 as shown in the figure If all the surfaces are smooth then the ratio of normal reaction between the block A and vertical surface of the cart and normal reaction between the blocks A and B is A B O a 2 m s

A train has 10 wagons each of mass 1000 kg attached to it They are being pulled by force 104 N Find out force exerted on last four wagons 1 4 10 N 2 4 104 N 3 5 x 104 N 4 5 x 10 N

Calculate the tension in the string shown in figure 5 E13 The pulley and the string are light and all surfaces are frictionless Take g 10 m s 1 kg 1 kg

m2 Figure 5 E7 To suf Consider the Atwood machine of the previous problem The larger mass is stopped for a moment 2 0 s after the system is set into motion Find the time elapsed before the string is tight again

30 When forces F1 F2 and F3 are acting on a particle of mass m such that F2 and F3 are mutually perpendicular then the particle remains stationary If force Fiis now removed the magnitude of acceleration of the particle will be F F 2 mF 1 F 121 3 F F mF 4 F m

Three masses of 1 kg 6 kg and 3 kg are connected to eac other with threads and are placed on a table as shown in figure What is the acceleration with which the system is Take g 10ms moving T 1 kg 10 Ti 3m 6 kg T 3 kg

11 A light string going over a clamped pulley of supports a block of mass M as shown in the figure The force on the pulley by the clamp is given by T Fret VT T Mg a 2 Mg c M m m mg m T IT M mg b 2 mg d g M m M

47 Two objects are connected by a light string passing over a light frictionless pulley as shown in the figure The object of mass m 5 0 Kg is released from rest at a height h 4 0 m above the table Find the maximum height above the table to which the 3 0 Kg object rises in m

12 A wire loop is rotated in a magnetic field The frequency of change of direction of the induced NEET 2013 e m f is 1 Twice per revolution 2 Four times per revolution 3 Six times per revolution 4 Once per revolution

A block of mass 1 kg is placed on the smooth inclined plane of inclination 37 force of 8 N is applied along the plane of inclined plane and perpendicular to greatest slope The acceleration of the block is a 10 m s b 8 m s c 6 m s d 2m s

Two blocks of masses 7 kg and 5 kg are placed in contact with each other on a smooth surface If a force of 6 N is applied on the heavier mass the force on the lighter mass is 6 N a 3 5 N e 6 N 7 kg b 2 5 N 5 kg c 7 N d 5 N Kerala PMT

In the arrangement shown in the figure the pulley has a mass 3m Neglecting friction on the contact surface the force exerted by the supporting rope AB on the ceiling is a 6 mg b 3 mg c 4 mg d None of the above B 2m

Nine forces are acting at a point as shown given figure The net force is F 40 40 F 1 F 3 F Fo F 40 40 F 40 F 40 F 40 F 40 40 F F 2 F 4 F F 10 2 20

Two equal heavy spheres each of radius r are in equilibrium within a smooth cup of radius 3r The ratio of reaction between the cup and one sphere and that between the two sphere is 3r3r

An inductor x 202 a capacitor x 802 and a resistance 802 is connected in series with an ac source The voltage output of A C source is given by v 10 cos 100ml The instantaneous p d between A and B is equal to xx 10 volt when it is half of the voltage output from source at that instant Find out value of x x 202 X 802 A 0 A555 11 B 80

A speed skater goes around a turn that has a radius of 26 m The skater has a speed of 14 m s and experiences a centripetal force of 450 N What is the mass of the s Number

28 The figure shows the position time graph of a particle of mass 40 kg What is the force acting on the particle for 0 t 4 s x m 3 0 1 30 N A 4 2 Zero t s

36 Two blocks A and B of masses 2m and m respectively are connected by a massless and inextensible string The whole system is suspended by a massless spring as shown in the figure The magnitude of acceleration of A and B immediately after the string is cut respectively is 1 g 6 2 3 a a 66 A 2m Bm 2 9 12 90 g 4 2

25 Calculate the tension in the string BC as shown www A 1 2mg cose 3 2mg sine 90 B 0 2 mg sine 4 mg cose 30 cted

Time taken by a body to slide down a rough surface inclined at an angle 8 is n times that required by the body to slide down the same distance on a smooth sur face inclined at also Find the coefficient of sliding friction between the body and the plane 1 2 tan

Find the acceleration of the 500 g block in figure 5 E18 100 g 50 g 30 500 g

9 In the arrangement shown in figure the ends P and Q of an inextensible string move downwards with uniform speed 1 Pulleys A and B are fixed The mass m moves P u upwards with speed a 2u cos 0 c 211 cos A a A 00 b M 11 Cos 0 d u cos 0 B u

For Pro Two containers of sand are arran Fig 6 381 The containers alone have negligible mass the sand in them has a total mass Mot the sand in the hanging containe H has mass m M Frictionless surface Acceleration of tension 2 Fig 6 381 To measure the magnitude a of the acceleration of the system a large number of experiments carried out where m varies from experiment to experiment but Mot does not that is sand is shifte between the containers before each trial 4 Massless pulley Hanging block H m 3 1 0 mMtot Fig 6 382 36 Which of the curves in graph correctly gives the accelerabi Mas mas as s mi

A 2 5 kg block is initially at rest on a horizontal surface A 6 0 N horizontal force and a vertical force pare applied to the block as shown in figure The coefficient of friction for the block and surface is 0 4 The magnitude of friction force when P 9N g 10 m s 1 6 0 N

1 A spring mass system is hanging from ceiling of an elevator The elevator is falling freely The elevator is suddenly stopped Find the amplitude of the resulting SHM with respect to lift 1 3 mg K mg 2K 2 4 2mg K 4mg K

A block of mass M 8 kg is connected to an empty bucket of mass 1 kg by a massless cord running over an ideal pulley The coefficients of static and kientic friction between table top and block are 0 5 and 0 4 respectively Sand is gradually added to the bucket until the block just being to slide The mass of sand added is g 10 m s 8kg Table Embudo

Two cyclists are in motion towards each other along a slightly inclined hill road The first cyclist starts with a velocity of 5 4 km h and attains a downhill accelera tion of 0 2 m s The second cyclist is under an uphill retardation of 0 2 m s2 after starting with a velocity of 18 km h If the initial distance between them is 130 m then when would they meet What would be their velocities at that instant 20 s 5 5 m s 1 m s

5 Consider the situation shown in figure 5 E9 All the surfaces are frictionless and the string and the pulley are light Find the magnitude of the acceleration of the two blocks 1 0 kg 3 m 5 m 4 m 1 0 kg

If the system is released from rest find total kinetic energy in joules of the blocks after t 2 sec of motion Take g 10 m s BOJ

A block of mass m is projected on a smooth horizontal circular track with velocity v What is the average normal force exerted by the circular walls on the block during its motion from A to B a my R B R A Fig 7 313 b my TR

Q23 The mass in the figure can slide on a frictionless surface When the mass is pulled out spring 1 is stretched a distance x and spring 2 is stretched a distance x The spring constants are k and k respectively Magnitude of spring force pulling back on the mass is A k x C k x k x seudo Forgo 000000000000000000000000 B k x k x D 0 5 k k x x

45 Acceleration of block A varies with time as shown in figure the value of coefficient of kinetic friction between block A and B is A 31 B F aA 5 m s 4 9 m s 30 the value of coefficient of kinetic friction between block A and Bis 1 0 5 0 6 None of these 2 4 10 s t s

A particle is projected from a point P 2 m 0 m 0 m with a velocity 10 m s making an angle 45 with the horizontal The plane of projectile motion passes through a horizontal line PQ which makes an angle of 37 with positive x axis and xy plane is horizontal The coordinates of the point where the particle will strike the line PQ is g 10 m s 25 A 10 m 6 m 0 m B 8 m 6 m 0 m 16x1 X4 V 50 2 C 10 m 8 m 0 m 30 18 D 6 m 10 m 0 m 2 2

The system shown Fig 6 388 is initially in equilibrium Masses of the blocks A B C D and E are respectively 3 kg 3 kg 2 kg 2 kg and 2 kg Match the conditions in Column I with the effect in Column II i ii iii Column I After spring 2 is cut a tension in string AB After spring 2 is cut tension in string CD After string between C and pulley is cut tension in string AB b C Spring 1 B E Fig 6 388 Column II Increases Decreases Remains constant Spring

18 The coefficient of static friction between A 0 4 and B is placed on a frictionless horizontal surface If a force of 250 N is applied on block A then acceleration of block B will be TITI 1 1 6 m s 3 2 5 m s2 B A 10kg 25kg F 250N 2 2 0 m s2 4 3 5 m s

33 A C 10 m m F 2mg 16 E F mg B 4 a a a a 10 E 2m In the figure the blocks A B C of mass m each have acceleration a a2 and a3 respectively F and F2 are external forces of magnitudes 2mg and mg respectively 1 a a a3 2 a a3 a 3 a a a a3 a2

11 A smooth ring A of mass m can slide on a fixed horizontal rod A string tied to the ring passes over a fixed pulley P and carries a block B of mass 2m as shown in the figure At an instant the string between the ring to the pulley makes an angle e with the rod The ring slides with a speed V then A V mgloss T my My Sue B 1 the block will descend with a speed V cos 0 2 the block will descend with a speed V cos 0 3 the initial acceleration of the ring when V 0 is 2g cos 0 1 2 cos 0 loration of the ring when V 0 is g cos 0 1 2 sin 0 Lot be the acceleration of the wedge an

A point moves along a circle with speed v at The total acceleration of the point at a time when it has traced 1 8th of the circumference is 1 8a 3 a 2 2a 4 4 4 R YAN A

A spanner of length 10 cm is used to unscrew a nut by applying a minimum force of 5 0 N Calculate the moment of force required Ans 0 5 N m ha rotated about an

Two blocks A and B each of mass m are placed on a smooth horizontal surface Two horizontal force F and 2F are applied on both the blocks A and B respectively as shown in the figure The block A does not slide on block B then the normal reaction acting between the two blocks is A F C F 3 B F 2 D 3F A m 30 B

26 A trolley is falling freely on inclined plane as shown in the figure The angle of string of pendulum with the ceiling of trolley is a equal to 1 0 3 90 Jo 2 90 0 4 0

R 0 30 A B 60 C A massive rope of uniform mass density and length is suspended from points A and B in vertical plane as shown in the figure Point C is the lowest point of the chord Given AC and BC The value of l l is

Investigators studying the effect of hitting a soccer ball with the head are using a force plate to look at the forces in ball collisions the force when the ball hits a player s head will be similar A 0 43 kg ball is launched at a force plate at 16 m s Smoothed data for the force versus time for the collision are shown in Figure 1 Figure Force N 3000 2000 1000 0 1 of 1 Part A At what speed does the ball rebound from the plate Express your answers with the appropriate units Uf 14 A Submit Value Units Provide Feedback Request Answer Next

10 A 958 N rocket is coming in for a vertical landing It starts with a downward speed of 25 m s and must reduce its speed to 0 m s in 8 0 s for the final landing a During this landing maneuver what must be the thrust due to the rocket s engines b What must be the direction of the engine thrust force

49 In the figure what should be mass m so that block slide up with a constant velocity a 1 kg c 0 5 kg A kg 37 0 5 m b 0 2 kg d 2 kg

In the arrangement shown in figure the strings are ideal The surface over which blocks are placed is smooth The tension developed in the string between the blocks of 4 kg and 2 kg is 7 N 4 kg 1 21 N 2 kg 1 kg 2 19 N F 28 N

5 In the system shown in Fig 6 295 pulleys are massless and frictionless Thread is inextensible Neglecting friction calculate the acceleration of the right wedge 0 m M M m 0

26 Sand is being dropped on a conveyor belt at the rate of M kg s The force necessary to keep the belt moving with a constant velocity of v m s will be AIPMT Prelims 2008 2 Mv newton 1 Zero 2 2Munouto Mv

59 A lift of mass 1000 kg is moving with acceleration of 1 m s2 in upward direction then the tension developed in string which is connected to lift is 1 9800 N 2 10 800 N 3 11 000 N 4 10 000 N