Circular Motion Questions and Answers

A ball of mass m moves inside a smooth spherical shell of radius R with velocity 2gR at A What is the direction of force acting on the ball When it reaches B PBQ R S

5 A certain wheel has a rotational inertia of 12 kg m As it turn through 5 0sec its angular vel increases from 5rad sec to 6rad sec If the net torque is constant its value is a 0 016N m c 0 57N m b 0 18N m d 2 1N m Ans d Sol Given that I 12kgm

Ex 2 A heavy particle of weight W attached to a fixed point by a light inextensible string describes a circle in a vertical plane The tension of the string has the values mW and nW respectively when the particle is at the highest and the lowest point of its path show that n m 6 et foul fren fac fere can

66 A thin convex lens of focal length 30 cm forms an image 2 cm high of an object at infinity A thin concave lens of focal length 20 cm is placed 26 cm from the convex lens on the side of the image The height of the image now is 1 1 0 cm 2 1 25 cm 3 2 cm 4 2 5 cm MAZB ZC ZD ZE ZH ZI ZQ ZR ZX PB GH WORK 12 04 2019 English

14 seconds Determine the magnitude a of the total acceleration of the car 9 seconds after the start Part 1 65 m Calculate the tangential component at of the acceleration

A particle suspended from a fixed point by a light inextensible thread of length L is projected horizontally from its lowest position with velocity 7gL 2 The string will slack after swinging through an angle 0 such that E equals a 30 120 b 135 d 150

56 A car is moving along a circular path of radius 500 m with a speed of 30 m s If at some instant its speed increases at the rate of 2 m s then at that instant the magnitude of resultant acceleration will be a 4 7 m s c 3 m s b 3 8 m s d 2 7 m s

A pendulum consists of a wooden bob of mass mand length 7 A bullet of mass m is fired towards the pendulum with a VI velocity v The bullet comes out of the bob with speed 3 and the bob just completes motion along a vertical circle The velocity v is 5gl a O 312 m 2 m 2 m m b 5gl m 3m d sant com 2 m

b of mass m connected to the end of an inextensible string of length I is released from position shown in figure If impacts of bob with smooth floor is perfectly inelastic Choose the correct option s 12 Floor The maximum height reached by the bob during subsequent motion is Maximum height reached by the bob during subsequent motion is zero Energy loss from the time duration bob is released to the time it reaches at its maximum height during subsequent motion is 3mgl 8 q no 5

3 An athlete completes one round of a circular track of radius R in 40 sec What will be his displacement at the end of 2 min 20 sec a Zero c 2R b 2R d 7 R

A disc of radius r rolls on a rough horizontal floor If velocity of its centre of mass is v then velocity of point p as shown in the figure OP r 2 and ZQOP 60 is Q 1 Vo Vo 160 V P 2 N 5 Vo 5

38 A car is moving with speed 108 km h on a large uniform horizon pavement perpendicularly towards a wall To avoid collision the driv takes a turn and finally runs the car parallel to the wall with the sa speed Coefficient of friction between the tyres and the pavement is C acceleration of free fall is 10 m s and all the load of the car concentrated on the front axle If the turning process is the fastest c on this pavement check validity of the following statements a The car follows a circular path during the turn b The car follows a parabolic path during the turn c Minimum radius of curvature of the path is 75 m d Initial distance of the wall must be greater than 75 2 m

8 A wave travelling along the x axis is described by the equation y x t 0 005 cos ax t If the wavelength and the time period of the wave are 0 08 m and 2 0s respectively then a and B En appropriate units are AIEEE 2008 A a 25 00 0 08 B a B C T 0 04 T 2 0 T B 1 0 T D a 12 50 20

A glass 1 5 cylinder of radius R and height h is placed on a table top and a point source S is placed at a height h above the centre as shown in figure The unilluminated area on the table top outside the cylinder is S 6 3 R 7TR 2 2 R 5 R h

A heavy particle of mass m is placed on the top of a smooth hemisphere also of mass m which is placed on a smooth horizontal plane as shown in the figure The system is released from rest Find the angle with the vertical where the particle will loose contact with the hemisphere m

A particle of mass m is tied to one end of a light inextensible string of length the other end of which is fixed as shown in the figure The particle is projected with a velocity u from the lowest position Find the net force acting on the particle when the string makes an angle with the vertical The acceleration due to gravity is g That I 721 A m 444

Three blocks of masses m m and m are connected by massless strings as shown in the figure on a frictionless table They are pulled with a force T 40N If m 10kg m 6kg and m 4kg The tension T will be 3 1 20 N m 2 40 N T m2 T2 m3 T3 3 10 N 4 32 N

3 A ball of mass m 0 5 kg is attached to the end of a string having length 1 0 5 m The ball is rotated on a horizontal circular path about vertical axis The maximum tension that the string can bear is 324 N The maximum possible value of angular velocity of ball in rad s is 2011 a 9 6 27 m b 18

A particle is moving along a circular path with a constant speed of 10 ms What is the magnitude of the change ins velocity of the particle when it moves through an angle of 60 around the centre of the circle 2019 Main 11 Jan I a 10 2 m s c 10 3 m s b 10 m s d Zero

A car of mass m wants to move on a circular turn of radius 120 m with 30 m s What should be the banking angle for circular turn g 10 m s O 45 O 53 O 37 O 15

The figure shows two cir B with masses 3m and m and radii R and 3R are hinged at their center respectively if a particle of m is attached to disc B at a distance 2R from its center and the system is released from rest Then the torque on disc A will be Assuming there is no slipping between the discs R 1 2mg 3 R 2 mg 2 B 3R 2R 3 2mgR 4 None of these A R 3m fiction Tolque due to

A section of fixed smooth circular track of radius R in vertical plane is shown in the figure A small block of steel is released from position A and leaves the track at B The radius of curvature of its trajectory when it just leaves the track at B is R OR 02 1 4 R R 2 None of these E D 30

A particle of mass m is moving in a horizontal circle of radius R with uniform speed v When it moves from one point to a diametrically opposite point its momentum does not change momentum changes by 2 mv kinetic energy changes by 1 2 mv2 kinetic energy changes by mv2

H A body of mass m rests on a horizontal floor with which it has a coefficient of static friction It is desired to make the body move by applying the minimum possible force F Find the magnitude of F and the direction in which it has to be applied

A cyclist riding the bicycle at a speed of 14 3ms 1 takes a turn around a circular road of radius 20 3m without skidding Given g 9 8 ms 2 what is his inclination to the vertical 1 30 2 90 3 45 4 60

For the given situation find tension T at point P in string Particle is moving in vertical circular motion 1 2 50 N 530 T 66 N R 1m Question Type Single Correct Type 37 10m s 1 kg

10 A particle is revolving in a circle of radius R with initial WORK speed v It starts retarding with constant retardation 4TR Hlaing The number of revolutions it makes before coming to rest is 1 1 3 4 27 2 3 4 none of these

Q5 A particle P is moving in a circle of radius a with a uniform speed v C is the centre of the circle and AB is a diameter When passing through B the angular velocity of P about A and C are in the ratio a 1 1 b 1 2 c 2 1 a 4 1

A particle is revolving in a circular path with increasing speed then angle 0 between the net force acting on the particle and centripetal force acting on the particle will be 0 0 90 8 90 0 0 0 180

equal masses m one secured at lower end A and the other at the middle of the rod at B The rod can rotate in verticle plane about a fixed horizontal axis passing through C What horizontal velocity must be imparted to the mass at A so that it just completes the vertical circle C l BOm

4 15 4 2 9 1 3 10 5 A Carnot engine whose efficiency is 40 takes in heat from a source maintained at a temperature of 500K It is desired to have an engine of efficiency 60 Then the intake temperature for the same exhaust sink temperature must be AIEEE 2012 1 efficiency of carnot engine cannot be made larger than 50 2 1200 K 3 750 K 4 600 K 500 125 1 0 4 340 B 22

A rod is rotating with an angular velocity of 3rt rad s The angle rotated by the rod from t 0 t time when it has an angular velocity of 24 rad s is given by a radian Fill in OMR sheet 2 a

A person at the origin O starts moving with a constant speed v along y axis At the same instant a particle of mass m starts from point P with a uniform speed v along a circular path of radius R as shown in figure Find the momentum of the particle with respect to the person as a function of time t m

A thin rod of mass m and length 1 is hinged at a point which is at a distance h h 1 above the horizontal surface The rod is released from rest from the horizontal position If e is the co efficient of restitution the angular velocity of rod just after collision will be h 1 m 1 2 m e 1 Option A B C 3 3g 8 6 3g 8 5 3g 8 h Rate this quest

A uniform rod of mass M and length L lies radially on a disc rotating with angular speed in a horizontal plane about its axis The rod does not slip on the disc and the centre of the rod is at a distance R from the centre of the disc Then the kinetic energy of the rod is Mo R m mo R Omo 2 24 12 None of these

Particle of mass 1 kg moving with constant speed 5 m s on a frictionless road as shown in figure Normal reaction by road on car NA NB at position A and B Radius of curvature at position A and B is same Sum of magnitude of normal at these position is 10 a in N Then the value of a is A B

Three friends ride a Ferris wheel with a diameter of 42m Their combined mass with each car of the Ferris wheel is 424kg When their car is at position A the steel support applies 680N force at the car at an angle of 40degrees with the horizontal What is the speed of the cars

A particle rotates in a circular path of radius 54m with varying speed v 4t 2 Here v is in m s and t in second Find angle between velocity and acceleration at t 3s A B C 15 30 45 Correct Answer

20 Q13 A particle moves along a circle of radius 2 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 CBSE AIPMT 2008 begin the tangential acceleration is

c 2 s d 15 s 9 A car of mass m starts from rest and acquires a velocity along east v vi v 0 in two seconds Assuming the car moves with uniform acceleration the force exerted on the car is eastward and is exerted by the car engine 3 b mv 2 d mv 2 tyres exerted by the road my c more than eastward exerted due to the 2 engine and overcomes the friction of the road exerted by the engine eastward and is due to the friction on the mv 2

mtG Objective NCERT 92 on the 73 One end of a string of length I is connected to a 78 In the question number 77 the force acting e particle is particle of mass m and the other to a small peg on a smooth horizontal table If the particle moves in a circle with speed v the net force on the particle directed towards the centre is where T is the tension in the string a T Eng c T b T d 0 74 The mass of a bicycle rider along with the bicycle is 100 kg He wants to cross over a circular turn of radius 100 m with a speed of 10 m s If the coefficient of friction between the tyres and the road 80 A stone of mass 5 kg is tied to a string of lengs 10 m is whirled round in a horizontal circle What is the maximum speed with which the stone can be whirled around if the string can withstand maximum tension of 200 N a 10 ms c 20 m s mut is 0 6 the frictional force required by the rider to cross the turn is a 300 N c 1200 N my a mg T b mg T c mg f Feet 75 A stone of mass m tied to the end of a string revolves in a vertical circle of radius R The net forces at the lowest and highest points of the circle directed 81 A disc revolves with a speed 33 rev min and has vertically downwards are Lowest Point T d mg T a 1 cm c 4 cm mv R my mv R b 600 N d 150 N Highest Point mg T mg T mg T mg T T and v denote the tension and speed at the lowest point T and v denote corresponding values at the highest point b 2 cm d 8 cm R 76 A small object placed on a rotating horizontal turn table just slips when it is placed at a distance 4 cm from the axis of rotation If the angular velocity of the turn table is doubled the object slips when its distance from the axis of rotation is mv b 2 ms2 d 4 3 m s 77 A particle is moving on a circular path of 10 m radius At any instant of time its speed is 5 m st and the speed is increasing at a rate of 2 m s The magnitude of net acceleration at this instant is a 5 m s c 3 2 m s a m F c 2mma F 79 The coefficient of friction between the tyres and the road is 0 1 The maximum speed with which cyclist can take a circular turn of radius 3 m withou skidding is Take g 10 ms a 15 ms c 30 ms b mxo d 2mx 7 a A c Both A and B b 3 mst d 10 m st b 15 m s d 25 m s a radius of 15 cm Two coins A and B are placed a 4 cm and 14 cm away from the centre of the disc If the coefficient of friction between the coins and the disc is 0 15 which of the coins will revolve with the record c 10 ms 83 In the question b B d Neither A nor B 82 A circular racetrack of radius 300 m is banked at a angle of 15 The coefficient of friction between the wheels of a race car and the road is 0 2 The optimum speed of the race car to avoid wear and tear on its tyres is Take tan 15 0 27 g 10 ms2 a 10 3 ms b 9 10 ms d 2 10 ms number 82 the maximum permissible speed to avoid slipping is a 18 6 m s b 28 6 m sl d 48 6 ms c 38 6 m sl 84 An aircraft executes a horizontal loop at a speed of 720 km h with its wings banked at 15 What is the radius of the loop Take g 10 m s tan 15 0 27 a 14 8 km b 14 8 m c 29 6 km d 29 6 m 8

The angular velocity of a body moving with a constant speed v in a circle of radius is given by a v r b vr c v r d r v An object at rest may have a momentum b potential energy c velocity d kinetic energy

c Both A and B d Neither A nor B 2 A circular racetrack of radius 300 m is banked at an angle of 15 The coefficient of friction between the wheels of a race car and the road is 0 2 The optimum speed of the race car to avoid wear and tear on its tyres is Take tan 15 0 27 g 10m s a 10 3 ms c 10 m s In the question b 9 10 m s d 2 10 ms 1 number 82 the maximum a c 88 A p an a upw time Tak a

An aircraft executes a horizontal loop at a speed of 720 km h with its wings banked at 15 What is the radius of the loop Take g 10 ms tan 15 0 27 a 14 8 km b 14 8 m c 29 6 km d 29 6 m

c 30 ms 80 A stone of mass 5 kg is tied to a string of leng is the maximum speed with which the stone can 10 m is whirled round in a horizontal circle What be whirled around if the string can withstand maximum tension of 200 N a 10 ms c 20 m s b 15 m st d 25 m s rey min 33 87

A particle of mass m is whirled in a vertical circle with the help of a thread If the maximum tension in the thread is double its minimum value then the value of minimum tension in the thread will be Option A B C 6 mg zero 3 mg Rate this ques

A long pipe 5 cm in diameter passes through a room and is exposed to air at atmo spheric pressure and temperature of 20 C The pipe surface temperature is 93 C Assuming that the emissivity of the pipe is 0 6 calculate the radiation heat loss per foot of length of pipe

A 0 028 kilogram rubber stopper is attached to one end of a string A student whirls the stopper overhead in a horizontal circle with a radius of 1 0 meter The stopper completes 10 revolutions in 20 seconds Determine the period T of the stopper Stopper 0 25 s O 0 5 s O 1 0 s 2 0 s 1 0 m Not drawn to scale

A uniform rod has mass m 2 kg and length I 13 m One end of the rod is pulled with a constant velocity of vo 34 m s along a frictionless horizontal floor in the negative x direction The other end is moving along a parabolic fixed curve The equation of the parabola is x 20y Find the angular velocity of the rod in rad s when the end point B is at 10 5 A y axis 0 0 B x 20y 10 5 x axis

14 Figure shows the electric lines of force emerging from a charged body If electric field at A and B are E and EB respectively and distance between A A and B is r then A 1 EA EB EB r 2 EA B