Circular Motion Questions and Answers

A particle of mass m is released from a height H on a smooth curved surface which ends into a vertical loop of radius R as shown m If is instantaneous angle which the joining the particle and the centre of the loop makes with the vertical as shown Then identify the correct statement s related to the normal reaction N between the block and the surface The maximum value N occurs at 0 0 The minimum value of N occurs at 0 for H 5R 2 The value of N becomes zero at 0 for all H Minimum value of H to complete vertical circular motion is 5R 2

A wheel of radius 20 cm has four forces applied 31 to it as shown in fig Then the torque produced by these forces about an axis which is passing through O and perpendicular to plane 8N 6N 1 5 4 Nm anti clockwise 2 1 8 Nm clockwise 3 2 0 Nm clockwise 4 5 4 Nm clockwise B 20cm 20 cm fa fangen 344 6N D 1 5 4 Nm 2 1 8 Nm afumad 3 2 0 Nm afernad 4 5 4 Nm afumad and and 34 34 318 9N

A motor car of mass 1000 kg runs over a bridge a t 48 km hr the roadway in the form of an arc of ra dius 20 m Find the reaction between the car and the road at the lowest point of the car 18686 7 N

A disc of radius Ris hinged at its centre such that it lies in a horizontal plane It rotates about the hinge with a constant angular velocity w A coin of mass mis placed at a distance of r from the centre The limiting value of angular velocity such that coin does not slip over the disc us coefficient of static friction k coefficient of kinetic friction Hog Hsg r kg

Topic SYLLABUS 2 1 Angular position of a particle is given 1 as 0 1 41 2 then average angular velocity from t 2s to t 4s will be 1 10 rad s 2 20 rad s 3 17 rad s 4 7 rad s feafa e 41 2 R adat 2 stufe an 1 10 rad s 3 17 rad s 2 20 rad s 4 7 rad s

3 17 rad s 4 7 rad s A particle moves with constant speed v along a 2 circular path of radius r and completes the circle in time T The acceleration of the particle is 1 2xv T 2 2xr T 3 2xr T 4 2av T 3 17 rad s fa FORUT 1 2av T 3 2x1 T V T 4 7 rad s fari uit 2 21 T 4 2av T

4 A solid sphere about any of its diameter 4 A thin wire of length L and uniform X linear mass density p is bent into a circular loop with centre at O as shown The moment of inertia of the loop about an axis XY is 1 3 pL 87 2 5pL 2 4 pL 167 3pL Y

An object moves in a circular path with a constant speed in the xy plane With the centre at the origin When the object is at x 2 m its velocity is 4 m s Then objects velocity at y 2 m is 1 4 m s i 2 4 m s 15 200 201 3 4 m s 4 4 m s 45 Using the data of Q 44 find objects acceleration when it is at y 2 m 1 8 m s i 2 8 m s i j 3 8 m s j 32 und 4 po 4 8 m s i

5 A large parking place has uniform slope of angle with the horizontal A driver wishes to drive his car in a circle of radius R at constant speed Coefficient of static friction between the tyres and the ground is u What greatest speed can the driver achieve without slipping Assume entire load of the car on the front wheels a gRtane e gR sin0 cos 0 b gRcot 0 d gR u cos 0 sin 0

A ring of linear mass density and radius R is rotated about its axis passing through its centre and perpendicular to plane of ring with constant angular speed w The tension in the ring is A Aw R 4 B w R 2 C Aw R 8 D Aw R

B OC 1 A small disc A placed on a frictionless tabletop is connected to a small protrusion B on the tabletop with the help of an almost inextensible elastic cord of relaxed length 1 There is a trap C in the table at distance n 0 5 times of 1 from the protrusion Initially the disc the protrusion and the trap are in a line and the cord is straight and relaxed as shown in the top view of the setup At what angle with the line AC must the disc be projected along the tabletop so that it enters the trap Diameter of the protrusion is negligible as compared to the length of the thread

A disc of radius R is hinged at its centre such that it lies in a horizontal plane It rotates about the hinge with a constant angular velocity w A coin of mass m is placed at a distance of r from the centre The limiting value of angular velocity such that coin does not slip over the disc us coefficient of static friction pk coefficient of kinetic friction O g 9 9 r

Passengers inside the gravitron ride stand against the walls of a rotating cylinder At time to the cylinder rotates at velocity v and at a later time t2 the cylinder has doubled its rotational speed What can be said about the centripetal acceleration of the passengers 4 The magnitude of the centripetal acceleration at time to is two times the magnitude of the centripetal acceleratin

14 A body runs on a circular path of radius R 28m with a constant speed u 4 m s Another boy starts from the center of the path to catch the first boy The second boy always remains on the radius connecting the center of the circle and the first boy and maintains the magnitude of his velocity V 4 m s If the time of chase is x sec then mark x T Answer Accepted error

The following table has 3 columns and 4 rows Based on table there are THREE questions Each question has FOUR options A B C and D ONLY ONE of these four options is correct Column I shows four situations with a small ball of mass m connected to an ideal string of length I and fastened to a point O whose acceleration if any is shown in the diagram Column 11 lists the minimum value of speed u with respect to point of suspension when the string is vertical in order for the mass to complete the circular motion in vertical plane Column ill lists the maximum tension throughout the circular motion corresponding to minimum speed Column 1 Column 3 1 III TV 19 3 O O O L l l 45 93 3 u 2g U 1 Column 2 3g 1 2ge 3 1 iv iii 5g 20g 3 Pick the correct combination from given options A 0 0 P B II iv R P 6 mg Q 4 3 mg R 7 mg S 8 mg ASSERTION REASONINE This question contains sta B C and D out of whi 1 2 STATEMENT 1 Work done by the because STATEMENT 2 Displacement of A Statement 1 statement 1 B Statement 1 statement 1 C Statement 1 D Statement STATEMENT A spring has pe because STATEMENT In compressing A Statemen statement B Statemen statement C Statemen D Statemen

Objective Question I Only one correct option 1 A person of mass M is sitting on a swing to length L and swinging with an angular amplitude 00 If the person stands up when the swing passes through its lowest point the work done by him assuming that his centre of mass moves by a distance 1 L is close to 2019 Main 12 April I a Mgl 1 0 c Mgl b Mgl 1 0 isning mu Castrome 20 000 0 2 2 d Mgl 1

29 The mass and diameter of a planet are twic those of Earth What will be the period oscillation of a pendulum on this planet if its is seconds pendulum on earth 1 2 s 2 2 2s 3 2 4 2 2 S Medi

Which of the following is are true about the uniform circular motion of an object a Direction of the velocity changes continuously b Acceleration is always directed towards the centre of circular path c Magnitude of velocity keeps on changing d Velocity remains constant The correct option s is are a and d a b and c Only b a and b

12 A circular disc of radius of gyration 20 cm at rest is dropped over another disc of same mass but double the radius of gyration rotating with 5 rad s If both the discs club together and rotate as one body about the same axis then the new combined angular speed of the discs is 01 rad s 02 rad s 03 rad s 04 rad s 4 points

3 7V 4 11V 4 If a planet is revolving around the sun in circular orbit with force Fay 5 2 where y is radius then square of period is propotional to 2 7 2 1 7 4 3 y 7 2

Two particles move with same speed v in x y plane Particle A moves on the circle of radius R centered at origin while particle B moves along the positive y axis At t 0 particle A is at R 0 and B is at the origin Average angular velocity of B as seen by A in the time interval is Find the value of a R AY VA B V YR 0 A X 2v

A block is placed in a groove made in the turntable having frictionless wall at 4cm from the centre of a turntable which is at rest The block fits tightly in the groove and is free to move in the groove The turntable is steadily accelerated at 2 5 rad s2 as shown in figure Coefficient of friction between the floor of groove and block is 0 1 The time in second at which the particle is about to slip is 4 cm

Two coaxial pipes of radius 1m and 1 2m are having a common horizontal axis A uniform solid spherical ball of radius 0 1m is fitted inside them as shown The inner surfaces are sufficiently rough so that there is no slipping anywhere On slight displacement the ball starts moving along the gap shown in the downward direction There are 2 possible cases 1 The inner pipe is held fixed but outer pipe is free to rotate 2 The outer pipe is held fixed but inner pipe is free to rotate All the 3 bodies have same mass 1 Kg both pipes ball When ball reaches the bottom the pipe which is free to rotate is rotating with A angular velocity w Let it be w in 1st case w in 2nd case w W 3 5 1 2m B 5 1m C 2 D

A carnival merry go round rotates about a vertical axis at a constant rate A man standing on the edge has a constant speed of 3 40 m and a centripetal acceleration of magnitude 2 49 m s Position vector locates him relative to the rotation axis a What is the magnitude of 7 What is the direction of when is directed b due east and c due south a Number b Units

A cylinder rolling over an edge without jump A cylinder of radius R is in pure rolling at speed u on a horizontal plane which is passing into an inclined plane of inclination angle a as shown in figure Find maximum value of u for which cylinder moves over to inclined plane without any jump at point O Sot If w is the angular speed of cylinder when it transits to incline plane then WE theorem by We use 1 2 mu 1 2 1 2m 1 1 mg R 1 cosa 1 2 1 2 MR w 1 43 1 Cosa 4 3R for cylinder not to take a jump at 0 we use N 0 just at this point w w R w g Cos 2 ing Cora L et 1 2 143 12 04 17 Casa 9 Cos 2 u 3R 7 Cas 4 Aus N mw R 2D

A stone of mass m tied to a string of length is whirled in a circle of radius r under th effect of gravity If its radial acceleration is p times the acceleration due to gravity g then it linear acceleration at a point on the circle where the string becomes horizontal P is ve B g p 1 C g p 1 2 A g p 1 D g p 1 2

A block of mass m moves on a horizontal circle against the wall of a cylindrical room of radius R The floor of the room on which the block moves is smooth but the friction coefficient between the wall and the block is The block is given an initial speed v The frictional force acting on the block as a function of distance traveled s is umy

A hollow cylinder is rotating with constant angular velocity about its horizontal axis A small ball moves in contact with its inner wall but leaves contact with it at a position as shown in the figure After losing contact it moves under gravity and hits the diametrically opposite point Assume friction to be sufficiently high so that it doesn t slide on the cylinder What is angle 0 diagram where it leaves contact A 0 30 C 0 37 0 R B 0 60 D 0 45

Online Mock Test Series for NEET 2020 18 A ball of mass m 0 5 kg is attached to the end of a string having length L 0 5 m The ball is revolved on a horizontal circular path about vertical axis passing through other end of the string The maximum tension that the string can bear is 324 N The maximum possible value of angular velocity of the ball in rad s is 1 9 3 27 2 18 4 36

If 400 2 of resistance is made by adding four 100 2 resistances of tolerance 5 then the tolerance of the combination is AIEEE 2011 1 15 3 5 2 20 4 10

A bob of mass M is suspended by a massless string of length L The horizontal velocity V at position A is just sufficient to make it reach the point B The angle 0 at which the speed of the bob is half of that at A satisfies 1 O e TL 2 O 4 3 O K N 31 4 B 0 A

This question has Statement I and Statement II Of the four choices given after the Statements choose the one that best describes the two Statements Statement Higher the range greater is the resistance of ammeter Statement II To increase the range of ammeter additional shunt needs to be used across it JEE Main 2013 1 Statement I is true Statement II is true Statement II is the correct explanation of Statement l 2 Statement I is true Statement II is true Statement II is not the correct explanation of Statement l 3 Statement I is true Statement II is false 4 Statement is falco Statement Lic falco Statomont II is truo

A ball is hanging from an inextensible string of length If the string is to become horizontal the bob should be projected horizontally with a velocity of 2gl DIf the bob is to reach a height of 2t above lowest point it should be projected horizontally with a velocity of 4gl If the bob is to reach a maximum angular displacement of 60 it should be projected horizontally with a velocity of g V If the bob is to reach a maximum angular displacement of 30 it should be projected horizontally with a velocity of

A particle originally at rest at the highest point of a smooth sphere is slightly displaced It will leave the circle at a vertical distance h below the highest point suc that Oh R Oh 2R Oh R 2 R h

A mass is attached at the lower end of a massless rod which is rotated in a vertical circle The length of rod is L What is the tension in rod at its lowest point Whe speed at lowest point is just sufficient to move the rod in circle m is mass of particle O4 mg 05 mg o 6 mg 3 mg

A motor car of mass 1000 kg runs over a bridge at 48 km hr the roadway in the form of an arc of radius 20 m Find the reaction between the car and the road at the lowest point of the car 18686 7 N

3 27 Two identical twins Tui and Kui are playing on a large merry go round in an amusement park The surface of merry go round is frictionless and is turning at a constant rate of revolution as the twins ride on it Tui sitting 2 m from the center of the merry go round must hold onto one of the metal posts round with a horizontal force of 90 N to attached to the merry go keep from sliding off Kui is sitting at the edge 4 m from the center With what horizontal force must she hold on to keep from falling off Ans 180 N Ans 3 3 2 3 CC A

8 A particle moves along a circular path of radius 2 m The distance travelled by particle in one revolution is 1 4 m 3 Zero 2 2 m 4 4 m

RIZONTAL CIRC A coin of mass m is stationary relative to a rotating disc axis passing pinning man having angular speed the centrifugal force on m is Omro mr w mr w wo P m 00

assage 1 massless A particle of mass m is revolving in a horizontal circle on a smooth table by an in extensible string if the initial speed of the particle is V and the particle has tangential acceleration of constant magnitude a After what time the tension of the string will be equal to T TR TR A a m 238 b a R V m Vo J6 b VBR V c 2gR V If V 0 then the distance covered by the stone till the string ruptures R gR 2a c FLITE Vo a If the breaking strength of the string is equal to weight of the stone The time after which the string will break C mv R 00 2aR d 2TR d m Vo d Yo 2gR V Vo a 2gR a

A particle of mass m is revolving in a horizontal circle on a smooth table by an in extensible massless string if the initial speed of the particle is V and the particle has tangential acceleration of constant magnitude a After what time the tension of the string will be equal to T TR Vo ca a TR m b a gR V Vo a m Vo c b o gR V Vo a mv R d c 2gR V 2TR If the breaking strength of the string is equal to weight of the stone The time after which the string will break m Vo Vo d 28R V

20 A particle moves along circle of radius TC m with constant tangential acceleration If the speed of the particle is 80 m s at the end of the second revolution after motion has begun the tangential acceleration is a 160 km s b 40mm s c 40 m s d 640 m s the normal and tangential

A rough vertical circle carrying a bead turns in its own plane about its centre with uniform angular velocity w Radius of circle is R and coefficient of friction between bead and circle is u with what minimum angular speed w should circle rotate so that bead never slips A B C 8012 00 f R g 1 R

21 The radius of circle the period of revolution initial position and sense of revolution are indicated in the fig Crabbe 3m 2 y t 4 sin 3 y t 3 cos YA 4 y t 3 cos y projection of the radius vector of rotating particle P is 1 y t 3cos2nt where y in m stolisur rt 2 P t 0 3 t 2 t 2 T 4s X where y in m where y in m where y in mor CO DE02 BOAI BONNEET UG 11 YRS 2009 2019 ENG 2019 NEET UG 01 PHYSICS P65

Radius of the curved road on national highway is R Width of the road is b The outer edge of the road is raised by h with respect to inner edge so that a car with velocity v can pass safely over it The value of h is 1 v b Rg 2 V Rgb 3 v R bg 4 v b R ERCISE P65

A rigid body rotates about a fixed axis with variable angular velocity equal to a 2bt at time t where a and are constants The angle through which it rotates before it comes to rest is b 2b 4b 2a2

A small bob of mass m is suspended from a vertical light string of length The bob is given a horizontal speed of 5g The difference in tension in the string at the topmost and bottom most point is 1 3mg 3 6mg 2 4mg 4 8mg

15 A massless ring hangs from a thread and two beads of mass m slide on it without friction The beads are released simultaneously from the top of the ring and slide down opposite sides If the angle from vertical at which tension in the thread becomes zero for the first time is 0 Find seco Physics m www m E 3

Stone tied at one end of light string is whirled round a vertical circle If the difference between the maximum and minimum tension experienced by the string wire is 2 kg wt then the mass of the stone must be 1 1 kg 2 6 kg 3 1 3 kg 4 2 kg

TU A particle moves along a circle of radius m with constant tangential acceleration If the velocity of the particle is 80 m s at the end of the second revolution after motion has begun the tangential acceleration is 1 40 m s 3 160 m s 2 640 m s 4 40 m s