Circular Motion Questions and Answers

41 A particle is revolving in a circular path of radius 25 m with constant angular speed 12 rev min The the angular acceleration of particle is 1 2 rad s 2 4 rad s 3 rad s 4 Zero

One fourth 397 A body is moving on a circle of radius 80 m with a speed 20 m s which is decreasing at the rate 5 m s at an instant The angle made by its acceleration with its velocity is 1 45 3 135 The distance of a particle moving on a circle of 2 90 4 0

While driving along an unbanked circular road a two wheeler rider has to lean with the vertical Why is it so With what angle the rider has to lean Derive the relevant expression Why such a leaning is not necessary for a four wheeler

A rigid triangular frame consists of three massless rods of length 2 5 m each and point masses of mass m each at vertex B and C respectively Frame is hanging vertically from point A about which it can rotate freely about an axis xx which is perpendicular to plane of frame as shown in figure Point of suspension of frame i e A is accelerating with constant acceleration a 3g 4 in horizontal direction and initially frame is at rest w r t support A Minimum initial angular velocity x 3 4 in rad s provided to system so that it can complete vertical circular motion in the frame of support A Calculate the value of x take g 10 m s X me B A a 3g 4 C

A small mass m is massless string whose other end is fixed at P as shown in figure The mass is undergoing circular motion in x y plane with centre O and constant angular speed If the angular momentum of the system calculated about O and P and denoted by Lo and Lp respectively then a Lo and Lp do not vary with time b Lo varies with time while Lp remains constant to a m c Lo remains constant while Lp varies with time d I and I both vary with time

Angular velocity of a particle is 0 where 0 is 0 2 angular position of particle Tangential acceleration of particle when it has covered I revolution in a circle of radius 2 m 1 4x 2 8x 3 2 4 16 aura etores energy in a

A particle undergoes uniform circular motion About which point on the plane of the circle will the angular momentum of the particle remain conserved 1 Centre of the circle 2 On the circumference of the circle 3 Inside the circle 4 Outside the circle

es simple while the st If two e period is F2 2 228 ergoing disha of fall of a it is en on J r Clock Andreas position and figure 1 1 2 y t 4 sin 4 3 y t 3 cos th y projection of the radius vector of rotating particle P is NEET 2019 ve t 1 y t 3 cos2nt where y in m where y in m P t 0 t 3 m 3 t 2 nt T 4 S X where y in m

17 In the given figure if body starts from height h and leaves the surface at height h then R A 0 0 e h h B cos 0 2 3 sin 0 C cos 0 3 2 sin 0 D cos 0 sin 0 2 nd whi 6 CO

A pilot of mass m can bear a maximum apparent weight 7 times of mg The aeroplane is moving in a vertical circle If the velocity of aeroplane is 210 m s while diving up from the lowest point of vertical circle then the minimum radius of vertical circle should be 1 375 m 2 420 m 3 750 m 4 840 m

13 A charge having q m equal to 108 C kg and with velocity 3x105 m s enters into a uniform magnetic field B 0 3 tesla at an angle 300 with direction of field Then radius will be love 2 cm 1 0 01 cm 2 0 5 cm 3 1 cm 2

5 The magnitude of change in velocity of a particle having speed v is v during a time interval At while moving in a uniform circular motion The magnitude of average force on the particle is proportional to

The graphs below show angular velocity as a function of time In which one is the magnitude of the angular acceleration constantly decreasing A C W 0 B D 0 1

7 The position vector of a particle R as a function of time is given by R 4 sin 2nt i 4 cos 2 t j Where R is in meters t is in seconds and i and j denote unit vectors along x and y directions respectively Which one of the following statements is wrong for the motion of particle 1 Path of the particle is a circle of radius 4 meter 2 Acceleration vectors is along R 3 Magnitude of acceleration vector is V R where v is the velocity of particle 4 Magnitude of the velocity of particle is 8 meter second

138 A disc is at rest at the top of a rough incined plane It rolls without slipping At the bottom of inclined palne there is a vertical groove of radius R In order to loop the groove the minimum height of incline required is 1 15R 4 2 9R 4

In the given circuit phase angle of ww 17 32 0 the voltage V has a with respect to V VL roo 10 2

The frictional co efficient between the board and the floor shown in figure is u Find the maximum force that the man can exert on the rope so that the board does not slip on the floor The mass of man is M and the mass of plank is m

D 21 31 C 21 31 A 21 31 A particle is moving on a circular path of radius r with uniform speed v The magnitude of change in velocity when the particle moves from P to Qis A 2vcos 40 7 B 21 33 0 B 2vsin 40 40 Q C 2vsin 20 Space for Rough Work D 2v cos 20

14 Which graph best represents the variation of radius r of a circular orbit of a satellite against its time perio r 1 1 1 3 3 2 3 y 2 2 4 4 4 T

In the given figure a 15 m s2 represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R 2 5 m at a given instant of time The speed of the particle is 1 5 7 m s 3 4 5 m s ac R 30 a 2 6 2 m s 4 5 0 m s

l On a train moving along east with a constant speed v a boy revolves a bob with string of length on smooth surface of a train with equal constant speed v relative to train Mark the correct option s A Maximum speed of bob is 2 v in ground frame G 4mv B Tension in string connecting bob is at an instant l C Tension in string is at all the moments my l D Minimum speed of bob is zero in ground frame V

Assume Earth s surface is a conductor with a uniform surface charge density o It rotates about its axis with angular velocity Suppose the magnetic field due to Sun at Earth at some instant is a uniform field B pointing along earth s axis Then the emf developed between the pole and equator of earth due to this field is R radius of earth C BOR Bored with CamScanner B BR D zero

50 A small block of mass m is projected horizontally with speed u where friction coefficient between block and plane is given by u cx where x is displacement of the block on plane Find maximum distance covered by the block b a c U eg 2u Jeg d U 2cg U 2 cg

A small cubical block of mass 1 kg is placed inside a rough rectangular groove made in a circular rough table as shown in the figure Coefficient of friction for all the rough surfaces is u 0 5 The table starts rotating clockwise with angular acceleration 1 rad sec in a horizontal plane about its axis Find the time in sec after which the block will start motion with respect to table Assume the size of 021 block slightly smaller then the width of groove 3m 74m

NEET I 2016 10 A particle of mass 10 g moves along a circle of radius 6 4 cm with a constant tangential acceleration What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 x 104 J by the end of the second revolution after the beginning of the motion 1 0 1 m s 3 0 18 m s ALLEN 14 2 0 15 m s 4 0 2 m s he loup A particle moves se by r cos oot Which of the fol 1 Velocity and a to r 2 Velocity and 3 Velocity is p is directed A 17 1

Three point masses each of mass m are joined together using a string to form an equilateral triangle of side a The system is placed on a smooth horizontal surface and rotated with a constant angular velocity o about a vertical axis passing through the centroid Then the tension in each string is 1 maw 2 3 ma 3 2 2 2 3ma mac 4 3 2 24

1 2 A 1kg block B rests as shown on a bracket A of same mass Constant forces F 20N and F 8N start to act at time t 0 when the distance of block B from pulley is 50cm Time when block B reaches the pulley is 121 1 2 k Fle 50 cm N CO B a Your 18 2 art

c anyone of them is valid If the wave length is 5000AU then wave number is a 2x106 b 2x105 number of waves in unit time is c 2x10 d d none frequency

5 An electron in the hydrogen atom jumps from excited state n to the ground state The wavelength so emitted illuminates a photosensitive material having work function 2 75 eV If the stopping potential of the photoelectron is 10 V then the value of n is AIPMT Mains 2011 1 5 3 3 2 2 4 4

Two satellites of earth are of equal masses They revolve in orbits of radius ratio 1 2 with same time period then their 1 Angular speeds are equal 2 Linear speed ratio is 1 2 3 Acceleration ratio is 1 2 4 All of these

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 sece www m m

A particle moves rectilinearly Its displ at time t is given by x at b where a and b are constants Its acceleration at time t is proportional to 2 1 1 1 a b c 23 d 3

Two particles describe the same circle of radius a in the same sense with the same speed v What is their relative angular velocity a vla c v 2a WIDE Shot on U10 Ourlivivo Al camera b 2v a d va

of a particle moving clockwise direction in a circle of radius R total acceleration at a given instant of time The speed of the particle is NEET Phase 2 2016 1 4 5 m s 3 5 7 m s R 30 va in the 2 5 m 2 5 0 m s 4 6 2 m s

A 650 kg elevator starts from rest It moves upward for 3 00 s with constant acceleration until it reaches its cruising speed of 1 75 m s i What is the average power of the elevator motor during this period On ii How does this power compare with its power when it moves at its cruising speed

A particle is moving along a circular path in xy plane When it crosses x axis it has an acceleration along the path of 1 5m s and is moving with a speed of 10 m s in ve y direction The total acceleration is y 2m X

A roller coaster is designed such that riders experience weightlessness as they go round the top of a hill whose radius of curvature is 20 m The speed of the car at the top of the hill is between AIPMT Prelims 2008 2 14 m s and 15 m s 4 16 m s and 17 m 1 13 m s and 14 m s 3 15 m s and 16 m s

Two particles move on a circular path one just inside and the other just outside with angular velocities and 50 starting from the same point Then A they cross each other at regular intervals of time when their angular velocities are oppositely 2 4 directed B they cross each other at points on the path subtending an angle of 60 at the centre if their angular velocities are oppositely directed loold bae xod e they cross at intervals of time if their angular velocities are oppositely directed 3w D they cross each other at points on the path subtending 90 at the centre if their angular velocities are in the same sense

6 A car is negotiating a curved road of radius R The road is banked at angle 0 The coefficient of friction between the tyres of the car and the road is g The maximum safe velocity on this road is S NEET 2016 OR a gR Hs tane 1 stane c g Hs tane R 1 tane b d d 9 Hs tane R1 stane gR2 Hs tane 1 tane R

23 A small stone of mass 50 g is rotated in a vertical circle of radius 40 cm What is the minimum tension in the string at the lowest point g 10 m s 1 6 N 3 3 N 2 2N 4 1 5 N

rom medium to medium 2 with plane interface if unit vectors in the direction of incident ray normal and the refracted ray are 39 represented by k and k respectively and the angles of incidence and refraction Do by 0 and 0 respectively then the Snell s law for refraction at the interface can be written in vector form as 1 k cos 0 os 0 COS 2 H k k H sin 0 sin 0 3 k k os 0 cos 0

A cord is wound over the rim of a flywheel of mass 20 kg and radius 25 cm A mass 2 5 kg attached to the cord is allowed to fall under gravity Calculate the angular acceleration of the flywheel AMU Engg 2012 2 a 25 rad s c 10 rad s b d 20 rad s 5 rad s

A clock is hanging on a wall The length of the second hand is 22 cm and the lowest that the tip of the second hand ever reaches above the ground is h cm The value of h is determined by the last three digits of your student number e g for 682304 h is 304 cm Student h cm a What are the equation of the axis amplitude and period in minutes of the function that represents the tip of the second hand s height above the ground 4 b Determine the equations of the sinusoidal functions both cosine and sine that represent the tip of the second hand s height above the ground Assume that at t 0 the time is 5 p m 4

1 A ball that is rotating in a circle on a string overhead is suddenly released The ball will move in what motion now 2 What makes the ball in problem 1 move in that motion after being released

3 A particle moves in uniform circular motion over a horizontal xy plane At one instant it moves through the points 5 0 m 4 0 m with a velocity of 5 0i m s and an acceleration of 10 0j m s 10 pts a Draw the circular path of the particle and label the velocity vector and the acceleration vector b Calculate the x and y coordinates of the center of the circular path c Calculate the period of rotation

m100 an Compositional Stoichiometry ng Molar Mass e molar mass of ethanol C H5OH a 45 07 b 38 90 c 46 07 d 34 17 e 62 07 NS c ne molar mass of Ca PO4 a 310 18 g mol b 87 05 g mol c 135 05 g mol d 118 02 g mol e 166 02 g mol NS a ng Between Grams and Moles using Molar Mass any moles of hydrogen sulfide H S 34 082 g mol are contained in a 35 0 g sample a 2 16 moles b 1 03 moles c 7 43 moles d 10 4 moles c 6 97 moles ANS b Name a 0 338 moles b 1 75 moles 2 96 moles 84 5 moles none of these an herbicide manufactured by Monsanto has the formula C H NO P How many pare there in a 500 g sample of Roundup Note this time you re not given molar calculate it c d c NIC I

Problem 2 A wheel with diameter 40 cm starts from rest at t 0 and rotates with constant angular acceleration 3 0 rad s a At what time does the wheel complete its second full revolution At this instant find b the speed of a point on the outer rim of the wheel and c the centripetal acceleration of a point on the rim

A hockey puck slides up and over smooth icy hill as shown The path of the puck is shown with the dashed line Assume no friction and assume that the hill has a round circular shape At the moment when the puck is at the top of the hill which free body diagram most accurately represents the directions and relative magnitudes of all the forces on the puck A B D H E

Problem 1 Jennifer sits in a Ferris wheel that is rotating at a constant frequency of 0 1 Hz At the highest point of her circular path the upward normal force the chair exerts on Jennifer is one fourth of her weight What is the radius of Ferris wheel Model Jennifer as a point mass

A mass m1 3 0 kg is connected by a light string that passes over a pulley of mass M 4 0 kg to a mass m2 2 0 kg sliding on a frictionless incline as shown in the figure There is no slippage between the string and the pulley The pulley has a radius of 25 cm and a moment of inertia of MR2 The angle is 60 degrees then what is the acceleration of m1 2 8 m s2 2 2 m s2 1 2 m s2 0 0 m s2 1 8 m s2 my