Circular Motion Questions and Answers

4 29 An electron is accelerated through a PD of 100V and then enters a region where it is moving perpendicular to a magnetic field B 0 2T Find the radius of the circular path Repeat this problem for a proton Ans 0 0167cm 0 7cm

A hemispherical bowl of radius R 0 1 m is rotating about its own axis which is vertical with an angular velocity w A particle of mass 10 kg on the frictionless inner surface of the bowl is also rotating with the same w The particle is at a height h from the bottom of the bowl The normal force on the mass when h R 2 is 2 N 05 N

A car turns a corner on a road of radius 4 60x10 1 m If the coefficient of static friction 0 90 what is the maximum speed in m s the car can negotiate the turn without sliding Note Your answer is assumed to be reduced to the highest power possible Your Answer

A pendulum bob of mass m with string length can swing in a vertical plane The bob is given an initial velocity from lowermost point in horizontal direction such that tension in rope and speed of pendulum becomes zero simultaneously Find maximum height rise by pendulur ptions 4 28 3

is calculated here because according to my c Iculation it is coming different from notes on e tell me why I am wrong 221 145 Example Find the angle between net acceleration a and the radial acceleration a at 2 s Given a 2t rad s w 0 R 1 m Solution a D In this case the angular acceleration is varying with time so to find the angle acceleration and the radial acceleration values of these accelerations at 2 s should do dt do 2t dt Integrating both the sides jde 2tdt 0 0 a t rads 2t 0 R t x1 p 9 12 16 ms a aR 2t x1 2t ms 9 1 4 ms tan 1 al 16 4 9 24 0 tan 4 wi dt 0 2txt rad 1 2 ang 4 t gads w R 1 L 2 1 e notes a net a 0

Two rods of equal length AC and BC are freely joined at C two ends A and B are pulled with speeds 2m s and 3m s respectively as shown in the figure at a particular instant shown in figure A The speed of the point C is n m s B The speed of the point C is m s C The angular speed of the rod AC is D The angular speed of the rod AC israd sec rad sec 2m s 60 3 60 B 3m s

Figure shows a uniform smooth solid cylinder A of radius 4m rolling without slipping on the 8kg plank which in turn is supported by a fixed smooth surface Block B is known to accelerate down with 6 m s B 6m s What is the angular acceleration of the cylinder in rad sec A 4m 8kg 2kg

4 Two insulated charged conducting spheres of radii 20 cm and 15 cm respectively and having an equal charge of 10 C are connected by copper wire and then they are separated Then 1 Surface charge density on the two spheres will be equal 2 Surface charge density on the 15 cm sphere will greater than that on the 20 cm sphere 3 Surface charge density on the 20 cm sphere will be greater than that on the 15 cm sphere 4 Both spheres will have equal charges

A particle performing uniform circular motion has O Radial velocity and radial acceleration A radial velocity and transverse acceleration Transverse velocity and radial acceleration Transverse velocity and transverse acceleration

A pure semi conductor has equal electron and hole concentration of n nn n 1016m 1016 m 3 Doping by indium increases n to 4 5 x in the doped semi conductor e 1022 m What is n 1 106m 3 n 3 2 2 10 m 3 I H 2 1022m 3 30 4 4 5 109 m 3

b An electron of kinetic energy 600 eV circle in a plane perpendicular to a uniform magnetic field The orbit radius is 12 5 cm Find a the electron s speed b the magnetic field magnitude c the circling frequency and d the period of the motion e through what potential difference would the electron have to be accelerated from rest to reach this kinetic energy

A particle of mass m is fixed to a string of length e The particle is given a horizontal velocity of 5gl at the lowermost position Calculate the net acceleration when the string becomes horizontal 1 10g 2 3g 3 g 4 2g

2 16000 N 3 4800 N 4 12000 N 14 Both A and B are thrown simultaneously as shown from a very high tower Then the correct option is 2 to Joh 4 2h 1600X7 1200 20 10 m s 10 m s 201 B sutth 20 23 t h 2 910 6 1 Distance between them is 20m at t 2s 2 Distance between them is 20 m at t ls 3 Magnitude of relative velocity of A w r t B is 20 m s at t 2s 7 26 4 Magnitude of relative velocity of A w r t B is 10 2 m s at t 3

135 A rod AB of length 2 m is hinged at point A and it s other end B is attached to a platform on which a block of mass m is kept Rod rotates about point A maintaining angle 0 30 with the vertical in such a way that platform remains horizontal and revolves on the horizontal circular path If the coefficient of static friction between the block and platform is 0 1 then find the maximum angular velocity in rad s of rod so that block does not slip on the platform g 10 m s

3 A car is moving on a horizontal road with curvature radius r Speed of the car is increasing at rate k If the car starts skidding at speed v coefficient of friction between the road and the car tyres is 75 v k k 2 v k gr g 1

A particle moves on a circular path of radius 7 m with constant speed 7 m s Match the Column I with column and mark the correct option given below Column l A The magnitude of displacement in metre of the particle during travelling the quarter of circle B The magnitude of average velocity in m s during travelling quarter of circle C The magnitude of acceleration in m s of the particle The magnitude of average accelerating in m s during travelling a quarter of circle P Q R S Column II 6 3 7 A 2 7 2

A toy car is moving on a circular track off radius 1 m Speed of the car is given by v t m s Mass of the car is 2 kg Match the column I with column II g 10 m s A B C D 84 du ans a r b r c q d p v t 1m Column I Time in sec at which resultant acceleration makes an angle of 0 TC 4 radian with tangential acceleration Rate of change of angle 0 shown in figure at above instant in rad sec is Friction force acting on the car at above instant in Newton If car starts sliding at t 3 sec Then coefficient of friction is P Q R S T Column II 1 10 2 1 10 2

Illustration 33 TU 2 Two projectiles are projected at angles 0 and 0 to the horizontal respectively with same speed 20 m s One of them rises 10 m higher than the other Find the angles of projection Take g 10m s Solution

A particle attached at one end of a vertical ideal string wher other end is kept fixed in vertical x y plane is given velocity Vo 3g Speed of the particle at its maximum height will be Vo 3gl

A spinning disk initially has an angular velocity of 12 rad s It experiences a constant angular acceleration of 3 0 rad s2 opposing this angular velocity How much time elapses before its angular velocity is 12 rad s in the direction opposite to its initial angular velocity 12 0 s 4 0 s 36 0 s 24 0 s 8 0 s

in a circular path with An object moves anticlockwise centre C Its acceleration vector continuously points towards O where AB is diameter Then correct statement is are A O C B A it speeds up from A to B slows down from B to A B it slows down from A to B speed up from B to A C its maximum speed is at A D its minimum speed is at A

A particle is moving in a circle of radius r centred at with constant speed v What is the change in velocity moving from A to B ZAOB 40 O O O O 2v sin 20 4v sin 40 2v sin 40 v sin 20

8 1 A starts sliding off the top of a smooth sphere of radius a The angle corresponding to the point at which the body breaks off the sphere is 0 then 0 is tr A 0 cos A C 0 cos a h A B a h a 0 4 B 0 cos ALLEN D 0 cos 2h a a 2h 10 The m radius throu perp 2kgr par edg fig

A 4 m 3 m B The rod AB is observed to be sliding down such that A slides along the wall and B stides along the ground At th instant shown end A is observed to have a downward velocity and acceleration of 2 m s and 3 m s respectively At the instant shown 1 Determine the velocity and acceleration of end B 2 Determine also the angular velocity and angular acceleration of the rod AB

10 A particle is moving with constant angular velocity on a circular path of radius R in the x y plane If observed from a reference frame moving with constant velocity along the z axis the particle will appear moving on a helical path of constant pitch h Making use of the given information what expression can be deduced for radius of curvature of the helical path h R 47 R h a R c b R h 47 R formation

A particle moves in a circle uniformly such that it completes a circle in 2 s During half a turn its centripetal acceleration changes by 6 m s Then A 2 GAMA 59 za S dage yuf 521 32 gufa 6 m s The radius of the circle is m 3 4 m Correct Answer B The magnitude of change in velocity during 1 s is m s 1 s a a Rm S C The tangential velocity of the particle is 64 K zef k m s Correct Answer The particle is moving with uniform acceleration

the lang swings in vertical circle as shown in figure total acceleration of the ball is ai bje when it is at angle 0 37 where a anda positive constant Find the magnitude of centr acceleration of the ball at the instant shown T axis system is shown in figure www A C 3a 4b 55 4a 3b 55 10 37 L B D 3a 4b 5 S 4a 3b 5 5

B A deuteron and an alpha particle having equal kinetic energy enter perpendicularly into a magnetic field Let ra and to be their respective ro Ta radii of circular path The value of is equal to Ta a b 1 c 2 H 2 d 2

28 180 Mark for Review 02 49 hr mir A mass m moves in a circle on a smooth horizontal plane with velocity vo at a radius Ro The mass is attached to a string which passes through a smooth hole in the plane as shown The tension in the string is increased gradually and finally m moves in a circle of radius Ro The 2

A bob of mass m is in equilibrium with the help of two inextensible string connected to fixed support The bob is slightly displaced perpendicular to the plane of figure and released The time period of oscillation of bob is P l A 27 FE g 25 B 2 B d C 25 12 1 l d D 2 41 d 2g

A particle of mass m is connected with a string of length 5 l One end of the string is fixed at O and other end is kept at a distance 3 l in a vertical plane at A as shown in figure OA is horizontal initially Particle is given a velocity of 8 lg in vertically upward direction Tension in the string at lowest point is Kmg Find the value of K 17 3l

38 An object of mass m moves with constant spee in a circular path of radius R under the action of force of constant magnitude F The kinetic energ of object is 1 FR 2 FR 4 1 FR

An electron and a proton having equal momentum enter in a unform magnetic field normal to the lines of force If the radii of curvature of circular path be r and r respectively then eta en un vieta ad ufak ark Gid af qan it fr m rp add

Two block P of mass 20kg and Q of mass 10kg are placed on a rough horizontal disk u 2 3 and are connected with a string which is along the diameter of disk as shown in the figure Then Here C is centre of the disc 20cm 50cm A The tension in the string when angular velocity of disc is 4 rad second is 80 3 N B Friction of 10kg block is 16 3 N when angular velocity of disc is 4 rad second C Friction of 20 kg block is 40 3 N when angular velocity of disc is 4 rad second D Maximum angular velocity of disc for no slipping of block is 5 rad second

An object moving with uniform acceleration has velocity of 12 m s in positive x direction when its x coordinate is 3 m If its x coordinate 2 s later is 5 m then its acceleration is 1 zero 3 16 m s 2 8 m s 4 6 m s

In system shown in the figure a block B of negligible mass is connected to a particle of mass 1 kg with a non stretchable string Now the hanging particle is given a velocity 8gH horizontally when system is at rest The initial acceleration of block B is 4K m s Then find the value of K g 10 m s H 2 m B 1 kg 2H

estion 9 7 3 1 3 4 1 6 The maximum angular speed of the electron of a hydrogen atom in a stationary orbit is 1 6 2 x 105 rad s 2 41 x 1016 rad s 3 24 x 1010 rad s 4 92 x 106 rad s A NB NA 2 NB

A circular loop of radius R carrying current I lies in x y plane with its centre at the origin The total magnetic flux through x y plane is A Inversely proportional to R YOU B O Directly proportional to R C Zero

Two particles A and B move in concentric circles of radii r and r respectively in such a way that A B and the centre of the circle O always lie on a straight line The ratio of their angular velocities O O 49 95 3 is

19 A pendulum consists of a wooden bob of mass III and length A bullet of mass m is fired towards the pendulum with a velocity v The bullet comes out of the bob with speed and the bob just V 3 completes motion along a vertical circle The vleocity v is 3 m 1 2 3 m 3 m 5gl 2 m m 5ge 3 m 24

20 A wheel rotates so that the angle of rotation is proportional to the square of time The first revolution was performed by the wheel for 8 sec Find the angular velocity 32 sec after the wheel started Hint Consider 0 kt find k

0 Angular momentum of a rigid body rotating about a fixed axis with angular velocity Is always in the direction of 2 Is always in the direction perpendicular to 3 May or may not be in the direction of 4 Is always in the direction opposite to direction of o

A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure The electric potential at the point O lying at a distance L from the end A is 0 A 1 3 L Q 8 E L Q 2 L 3Q 4 EL O In 2 B

The potential energy of a particle of mass m at a distance r from a fixed point 0 is given by r kr2 2 where k is a positive constant of appropriate dimensions This particle is moving in a circular orbit of radius R about the point O If v is the speed of the particle and L is the magnitude of its angular momentum about 0 which of the following statements is are true A v B v k 2m k R R m C L mkR D L mk 2 R

2 8 A particle is attached to a fixed point by a light string of length C It is held with the string taut and horizontal and let go Prove that i when the string makes an angle a with the horizontal the resultant acceleration a g 1 3sin a and ii When it is below the fixed point its velocity v 2 gl

In a non uniform circular motion of a particle A Angular acceleration of particle is perpendicular to acceleration of particle B Angular acceleration of particle is perpendicular to velocity of particle C Angular velocity of particle is perpendicular to acceleration of particle D Angular velocity of particle is perpendicular to velocity of particle

A motor car is travelling at 60 m s on a circular road of radius 1200 m It is increasing its speed at the rate of 4 m s Find the acceleration of the car is in m s You are shown a photo of a car driven on a vertical inside wall of a huge cylinder with a radius of 10 m The coefficient of static friction between the car tires and the cylinder is 0 25 The minimum speed in m s at which the car can be driven like that is 5x Find x

A particle of mass m moves in the XY plane with a velocity v along the straight line AB If the angular momentum of the particle with respect to origin O is LA when it is at A and Lg when it is at B then 2007

A ring of mass M hangs from a thread and two beads of mass m slide on it without friction as shown The beads are released simultaneously from the top of the ring and slide down opposite sides The minimum value of m for which the ring rises and the angle E at which it happens are B 1 5M 3M

This question has statement 1 statement 2 Of the four choices given after the statements choose the one that best describes the two statements Statement 1 When moment of inertia I of a body rotating about an axis with angular speed o increases its angular momentum L is unchanged but the kinetic energy K decreases if there is no torque applied on it AIEEE 2012 Online Statement 2 L I w kinetic energy of rotation 1 10 Io 2 1 Statement 1 is false Statement 2 is true 2 Statement 1 is true Statement 2 is true and Statement 2 is not the correct explanation of statement 1 3 Statement 1 is true Statement 2 is false 4 Statement 1 is true Statement 2 is true and Statement 2 is the correct explanation of Statement 1