Circular Motion Questions and Answers

A water fountain on the ground sprinkles water all around it If the speed of water coming out of the fountain is V the total area around the fountain that gets wet is Question Type Single Correct Type 1 2 V 77 2 g 4 V g 3 T k V 75 g V4 a2

The radii of circular paths of two particles of same mass are in ratio 3 4 ther what will be ratio of speed if they have some magnitude of centripetal force 02 3 O32 O 3 1 45

A body executing uniform circular motion has position vector and accelera vector Are perpendicular to each other Are along same direction Are in opposite direction May be inclined at any angle

26 Obtain an expression for the acceleration of a particle performing circular motion Explain its two components OR For a particle performing uniform circular motion v xr Obtain an expression for the

6 A section of fixed smooth circular track of radius R in vertical plane is shown in the figure A block is released from position A and leaves the track at B The radius of curvature of its trajectory just after it leaves the track at B is A 53013701 I iO B

D Og mass on a 20 cm long string oscillates as a pendulum It has a speed of 0 28 m s as it passes through the lowest point What maximum angle in rad does the pendulum reach g 9 8 m s Assume the motion is simple harmonic motion

Why is centrifugal force called a pseudo force Calculate the centripetal force acting on a small mass of 0 25 kg rotating 1800 revolution min on a radius 200 mm Why does a cyclist bend inwards while riding along a curved road 2 2 2 2

3 A particle is moving in a circle of radius 3 m with an angular velocity 2 radian per second in clockwise direction as shown Find acceleration of particle at point Q y Q 60 X 1 61 6 31 m s 2 6 31 61 m s 3 61 6 31 m s 4 61 6 51 m 2

A simple pendulum is oscillating without damping When the displacement of the bob is less than maximum its acceleration vector a is correctly shown in IIT JEE Scrrening 2002 1 3 a a 2 a

Two forces of unequal magnitude simultaneously act on a particle making an angle 0 120 with each other If one of them is reversed the acceleration of the particle is becomes 3 times Calculate the ratio of the magnitude of the forces

particle starts moving along a m with a constant tangential acceleration If he velocity of the particle is 120 m s at the end of he second revolution after the motion has begun me tangential acceleration is 1 40 m s 35 m s 45 m s 50 m s2 adius

5 A uniform circular disc of radius 50 cm at rest is free to turn about an axis which is perpendicular to its plane and passes through its centre It is subjected to a torque which produces a constant angular acceleration of 2 0 rad s2 Its net acceleration in m s at the end of 2 0 s is approximately 1 8 0 2 7 0 3 6 0

The resultant of two vectors of magnitudes 3A and 2A is R If the first vector is doubled then the magnitude of resultant is also doubled The angle between two vectors is 1 60 3 90 2 120 4 180

Q8 A particle starts from rest at t 0 and starts moving on a circular path of radius m with 4 TC tangential acceleration 6 m s2 where t is in seconds Calculate acceleration of the particle when it completes one revolution in m s Options 12 167 1 12 1 97 12 16 1718 16 skippec

An inductor 20 mH a capacitor 100 F and a resistor 500 are connected in series across a source of emf V 10 sin 314 t The power loss in the circuit is 1 0 79 W 3 1 13 W A metallic rod of mass per unit length 0 5 kg m 2 4 0 43 W 2 74 W

III A beam of electron passes undeviated through two mutually perpendicular electric and magnetic fields If the electric field is cut off and the same magnetic field is maintained the electron move in a circular path of radius 1 14 cm determine the ratio e m if E 8 kV m and B 2 x 10 T

3 1 a b only 2 a b c 3 a b c d only C D INWE V The figure shows the result of an experiment involving photoelectric effect The graph A B C and D relate to a light beam having different wavelength Select correct a Beam B has a highest frequency b Beam C has longest wavelength c Beam A has highest rate of photoelectric emission d Highest momentum is possesed by some electrons emitted by B

i A vehicle is moving at a speed of 30 m s on a circular road of radius 450 m Its speed is increasing at a rate of 2 m s The acceleration o particle at this instant is 1 2 8 m s 3 2 m s2 2 4 m s 4 Zero

Two particles are attached to light s tring the masses are rotated at const ant angular speed of 5 Radian per se cond about a point A the surface is h orizontal and smooth the ratio of ten sion the inner strength to Outer one i S Q 41 Code A Circular Motion Tension 1 Two particles are attached to light strings as shown in figure The masses are rotated at constant angular speed of 5 radian per second about point A The surface is horizontal and smooth The ratio of tensions in inner string to outer one is 15 4 3 4 3 M 2 3 4 4 1 1 2 M

JIPMER 2001 02 a 250 N c 1000 N A ball of mass 0 25 kg attached to the end of a string of length 1 96 m is moving in a horizontal circle The string will break if the tension is more than 25 N What is the maximum speed with which the ball can be moved CBSE PMT 1998 b 750 N d 1200 N a 14 m s b 3 m s d 5 m s c 3 92 m s A body of mass 5 kg is moving in a circle of radius 1m with an 61 62 Find the maximum circular track of rac road and tyre is 0 2 a 0 14 m s c 1 4 km s A car when passes which is equal to Mv r a Mg

c 99 m s d 86 m s The second s hand of a watch has length 6 cm Speed of end point and magnitude of difference of velocities at two perpendicular positions will be RPET 1997 b 8 88 and 4 44 mm s d 6 28 and 8 88 mm s a 6 28 and 0 mm s c 8 88 and 6 28 mm s A sphere of mass m is tied to end of a string of length I and rotated through the other end along a horizontal circular path with speed v The work done in full horizontal circle is 67 68 An unbanked curve which a 0 75 a c A wheel then the diameter of a 1 5 m HINT

A particle is placed inside a hemispherical bowl which rotates about its vertical axis with constant angular velocity w It is just prevented from sliding down when OP is inclined at 45 with the axis O is the centre of the sphere and P is the position of the particle The radius of the bowl is 10 2 m and coefficient of friction between the particle and the bowl is 0 5 Find the magnitude of angular velocity w assuming g 10 m s A 1 3 R P Correct Answer

A solid sphere rolling on a rough horizontal surface with a linear speed v collides elastically with a fixed smooth vertical wall The speed of the sphere after it has started pure rolling in the backward direction is A B C D 2v 7 3v 7 Zero Correct Answer

A particle is suspended from a fixed point by a string of length 5m It is projected from the equilibrium position with such a velocity that the string slackens after the particle has reached a height 8m above the lowest point So height the particle can rise further A B C D 0 80 m 0 96 m 96 m 0 48 m Correct Answer

A wheel is rotating at 720 rpm and the power supply is swtiched off the retardation is produce is 2 radian sec 2 How much time will it take to stop and how many revolution will it will make till it s stop

1 The angular position of a particle revolving about an axis is given by 0 t t 3t 4 radian Find the acceleration of the particle at time t 2s Given radius of circular path is 1 m 1 2 m s 2 1 m s 3 5 m s 4 5 m s

A stone attached to a rope of length 1 80 cm is rotated in vertical plane with a frequency n 240 r p m At the moment when the velocity of the stone is directed vertically upwards the rope ruptures To what further height does the stone rise The air resistance should be neglected a 10 3 m b 41 2 m V YW V 80 y 9 56 20 20 6 m v 3 2gh d 24 9 m Wz

A particle moves in a circle of radius 4 cm clockwise at constant speed of 2 cm s If and y are unit acceleration vector along x and y directions respectively in cm sec The acceleration of the particle at the instant half way between P and Q is given by m 4 x y b 4 x y c QX x y 2 8 9 d 4 P U 20 5 Oc 2 0

When the angular velocity of a uniformly rotating body has increased thrice the resultant of forces applied to it increases by 60 newton Find the accelerations of the body in the two cases The mass of the body m 3 kg a 2 5 ms 2 7 5 ms 2 c 5 ms 2 45 ms b 7 5 ms 2 22 5 ms d 2 5 ms 2 22 5 ms 2

This question is from NEST 2020 ses sion 1 answer is there in similar quer ies but there it is given 2nd option w hereas here the answer is given as 4t h option pls verify Reply to the same question sent on Aug 12 2020 Q 5 A spherical bob hangs from a light inextensible string and moves in a horizontal circle with string making angle with the vertical The length of the string is then very slowly increased so that the motion is circular at all times to a good approximation If h is the height from center of the circle to the pivot and r is the radius of the circle then hor The value of a is X 3 X2 1 X 2 4 Ans 4

A particle of mass rotates in a circle which has a vertical boundary of radius 0 2 meter rotating in horizontal plane Mass of the block is 200 gram It takes 40 second in one complete revolution Find the normal force on block 1 9 8 10 N 2 9 8 10 2N 1 N mo R 2 0 2 47 R 0 2 4 9 8 1600 9 8 10 N 0 2 3 9 8 N 4 9 8 10 N INSTI

5 Closed organ pipe having length 48 cm and diameter 5 cm is sounded in its fundamental mode The wavelength of displacement wave produced in the pipe is 1 0 99 m 3 1 98 m 2 1 92 m 4 0 495 m

A When a body moves on a curved path with increasing speed then angle between instantaneous velocity and acceleration is acute angle R When the speed is increasing its tangential acceleration is in the direction of instantaneous velocity

D A Uniform circular motion is accelerated motion still speed remains unchanged R Instantaneous velocity is always normal to instantaneous acceleration in uniform circular motion

A thin string is wrapped several times around a cylinder kept on a rough horizontal surface A boy standing at a distance from the cylinder draws the string towards him as shown in figure The cylinder rolls without slipping The length of the string passed through the hand of the boy while the cylinder reaches his hand is A B 2 C 3 D 4

19 Starting from rest if a car accelerates uniformly at the rate of 1 m s for some time and then decelerates uniformly at the rate of 2 m s and finally comes to rest after a journey of 1 minute The maximum possible speed of the car during this journey is 1 10 m s 2 20 m s 3 30 m s 4 40 m s

A ladder stands on a frictionless floor and leans against a frictionless wall It is initially held motionless with its bottom end an infinitesimal distance from the wall It is then released where upon the bottom end slides away from the wall and the top end slides down the wall When it loses contact with the vertical wall then find angle made by rod with horizontal direction at this instant 12 B 0 Sin 3 D A 12 0 Cos 3 C 0 Cos 11 I3 0 Sin 11 3 1

angular acceleration a as shown in figure then Answer A B C Your Attempt Correct answer the constant magnitude of velocity of the particle in the first t sec 2a tR the angle subtended by path followed by the particle at the centre of the circle in the first t sec a t magnitude of its acceleration in the first t sec 2a R CL

A particle starts moving from the point 1 2 3 under velocity li 23 3k for two seconds After that it moves under velocity 11 2j 3k for the next two seconds What is the coordinate of the final point A 5 2 5 C 1 2 15 A B 4 Correct Skipped By You B 5 2 15 D None of these

Figure shows a bar of mass m moving with a constant speed vo on horizontal surface around a semi circular fence of radius R The average normal force acting on the bar due to contact with the fence is given by a Fill the value of a Consider all surfaces to be smooth R

25 For a particle in uniform circular motion the acceleration a at a point P R 0 on the circle of radius R is here 0 is measured from the X axis v a b c 10 WAWA R v cos e sine i R sin ei cos e i 2 v v R v R cos e j sin e j

33 A particle is moving along a circular path of radius 5 m s The average 5 m with a constant speed of 2 acceleration over a quarter circle is 10 1 it 3 5 TC m s m s 2 44 5 2 TC 5 2 m s m s portain height

Matching List Type This section contains 4 multiple choice questions Each question has matching lists The codes for the lists have choices A B C and D out of which ONLY ONE is correct 17 A particle is performing a motion in x y plane at time t r is the position vector of particle at any time t and r 0 is the polar coordinate of that particle at that time t Match List I with List II List I List II P Q R S Codes Motion along straight line along x axis Circular motion along circle whose centre is O and radius is r Simple harmonic motion along x axis whose extreme points are A B and O is mean position only consider motion to the right of point O Elliptical motion along ellipse whose centre is O P 3 A B 3 C 2 Q 1 3 3 R 4 1 4 S 2 2 3 O O 0 P r 0 03 B X P r 0 B X X 1 dr 5 dt 9 2 3 4 dr dt 0 de dt dr 11 0 de dt 0

44 A particle is moving with constant speed 10 m s in x y plane as shown in the figure The magnitude of its angular velocity about origin at this instant is x and y are in m 012 der y 4 1 1 4 rad s 2 1 2 rad s 3 1 6 rad s WZD 205 10 m s 5 3 33 X 3 28 33 25 0 83 S 1 10 t g t E

A small body of mass m is placed at the top of a smooth sphere of radius R placed on a horizontal surface as shown Now the sphere is given a constant horizontal acceleration ao g The velocity of the body relative to the sphere at the moment when it loses contact with the sphere is A C gR 3 5gR 3 B D 2gR 3 7gR 3 ao g

owing questions A flywheel is spinning about its axis of symmetry has weight W and it rotates with a constant angul speed w Moment of inertia of the flywheel about the axis of its spin axis of symmetry is I and th distance of the flywheel from the pivot is r 7 8 The rotation of flywheel axis about the pivot is called A gyration C dipping precession D none of these The torque due to weight of the flywheel when the flywheel is rotating about its axis ALOnly changes the magnitude of its angular momentum BOnly changes the direction of angular momentum C Changes both direction and magnitude of D none of these

A charge particle is revolving around a central charge with frequency 2 x 1015 Hz Find current due to motion of charge particle radius of orbit is 0 6 A q 2 x 10 18 C m 2 x 10 30 kg 1 1 MA 2 4 mA 3 4 x 10 5 A 4 zero

Block is free to move inside a vertical fixed smooth tube shown in the figure Choose correct option s Block will oscillate when v 2gR Block will complete vertical circular motion when v Block will complete vertical circular motion when v 4 5gR 6gR Block will complete vertical circular motion when Vo 2gR R Block

A particle of mass m connected to a string of length l which is rotating in a vertical circle such that the ratio of the maximum to the minimum tension in the string is 2 1 then find out the speed of the particle at the bottom most point O 13ge 12ge O 11ge 10ge

Q14 A blue ball of mass 5kg is tied to a string of length 2m and swung in a loop with a velocity of 1 m s A red ball of mass 10 kg is tied to a string of the same material and length and swung with the same velocity in a loop Then O A The centripetal acceleration of red ball is double that of blue ball O B The centripetal acceleration of red ball is half of that of blue ball O C The centripetal acceleration of red ball is 4 times as that of the red ball O D The centripetal acceleration is the same for both balls