Circular Motion Questions and Answers

57 A particle of mass m moves with constant speed v on a circular path of radius r as shown in figure The average force on it during its motion from A to B is 1 2 3 3mv 2 r mv r 2 3mv K B 30 C A

s in a uniform magnetic field perpendicular to its plane with the uniform 9 A wheel has three spokes and axis of rotation of the wheel parallel to the magnetic field When the wheel rotates with a angular velocity w the emf induced between the center and rim of the wheel is e If another wheel having same radius but with six spokes is kept in the same field and rotated with a uniform angular velocity o 2 the emf induced between the center and the rim will be 1 e 2 e 2 3 2e 4 e 4 24 Figure sh which is directe induced current

tration 13 A car starts from rest with a constant tangential acceleration a in a circular path of radius r At car skids find the value of coefficient of friction ational force

A bobbin rolls without slipping over a horizontal surface so that the velocity v of the end of the thread point A is directed along the horizontal A board hinged at point B leans against the bobbin Fig 4 The inner and outer radii of the bobbin are r and R respectively Determine the angular velocity o of the board as a function of an angle a

A small sphere of mass m is connected by a string to a nail at O and moves in a circle of radius r on the smooth plane inclined at an angle with the horizontal If the sphere has a velocity u at the top position A Mark the correct options B C 90 U O A 0 37 Minimum velocity at A so that the string does not get slack instantaneously is 3 5gr Tension at B is 9mg 5 if the sphere has the required velocity as in option A

If 90 of radioactive sample is left undecayed after t seconds has elapsed what percentage of initial sample will decay in total time of 2t seconds O 25 O 19 hr min O 15

An electric dipole is kept at origin as shown in the figure The point Q R are on a circular arc of radius r If the electric fields at P Q and A respectively are E E E then select the correct option r d 2 2 All of those R

radius R placed freely on a horizontal smooth surface as shown in the figure A particle of mass m is connected to the circumference of the disc with a massless string Now an impulse J is applied on the particle in the directions shown by dotted line The acceleration of centre of mass of the disc just after application of impulse is If J 10N sec m 2R 10kg R 25cm R 2m

6 m long see saw remains horizontal when two children weighing 20 kg and 30 kg respectively sit at two ends Where is the see saw supported A 3 6 m from 20 kg B 2 6 m from 30 kg 4 m from 20 kg 4 2 m from 30 kg C D

A passenger sitting in a bus moving along a circular path experiences a force which is A opposite to the acceleration of the bus B in the same direction as that of the acceleration of the bus along the direction of motion of the bus opposite to the direction of motion of the bus C D

6 A particle of mass m 5 units is moving with a uniform speed v 3 2 units in the XY plane along thene y x 4 The magnitude of the angular mom tum about origin is a zero b 60 unit c 7 5 unit d 40 2 unit oilluant

A square of side x m lies in the x y plane in a region where the magnetic field is given by B Bo 31 4 5k T where B is constant The magnitude of flux passing through the square is a 5B Wb b 3B Wb d Box Wb c 2B x Wb

Consider a circular turn on a highway where angle of banking is more than angle of repose A car on this turn can move with a constant speed vo without help of friction Taking advantage of friction it can achieve a maximum speed Umax but cannot reduce its speed lower than a minimum speed Umin Which of the following conclusions can you draw from the given information a vo 0 5 Umax Umin c vo 0 5 Umax Umin b Vo 0 5 Umax Umin d It depends on coefficient of static friction

QA uniform disc of mass m and radius R is hanging from a rigid support and is free to rotate about a horizontal axis passing through its center in vertical plane as shown An insect of mass m falls vertically and hits the disc at a point at horizontal diameter with a velocity vo and sticks on it calculate the minimum value of vo so that the disc completes the vertical circular motion m

As shown below AB represents an infinite wall tangential to a horizontal semi circular track O is a point source of light on the ground at the center of the circle A block moves along t circular track with a speed v starting from the point where the wall touches the circle If the velocity and acceleration of shadow along the length of the wall is respectively and a therm B A V P COS B V sec see tan C n

When a bucket containing water is rotated fast in a vertical circle of radius R the water in the bucket doesn t spill provided that the bucket is a whirled with a maximum speed of 2gR b whirled around with a minimum speed of 1 2 GR c having a rpm of n 900g R d having a rpm of n 3600g R

A point object of mass 0 5 kg is moving on a circular track of radius Im The position vector of the object at some instant with respect to the center is given by i m The position vector of the particle at that instant with respect to the point P is a p m b 3 1 fm c 10m d 2 3 1 2 m P 1m 120

2 m s 4 m s cular motion the on the circle of com x axis a horizontal al force equal 22 A particle of mass 1 kg is suspended from a ceiling through a string of length 10 2 m The particle moves in a horizontal circle Find its time period 1 2x sec 2 sec 3 T 2 TI sec 4 1 sec r 45 joined together by a

5 A car moves of a constant speed on a road a shown in figure If N and Ng are normal reactins at A and B then B 1 N N 3 N NB A B 2 N NB 4 Data insufficient

A homogeneous slender prismatic bar of length and weight Wis hinged at its lower end and can rotate freely in the vertical plane If the bar is released from rest in the unstable equilibrium vertical position and falls under the influence of gravity calculate the horizontal reaction at the hinged support when the bar makes 30 with vertical

A particle moves in a circular path with decreasing speed Choose the correct statement 1 Angular momentum remains constant 2 Acceleration a is towards the center 3 Particle moves in a spiral path with decreasing radius 4 The direction of angular momentum remains constant

c 1 54z 54 The height of a swing changes during its motion from 0 1 m to 2 5 m The minimum velocity of a WW boy who swings in this swing is a 54m s c 3 14 m s b 1 0 Hz d 2 0 Hz 55 Starting from y A sin wt or y A cos aut b 4 95 m s d Zero

A string of length 1m is fixed at one end and carries a mass of 100 g at the other end The string makes 2 revolutions per second around vertical axis through the fixed end What is the tension in the string 1 16 N 100g N 1m 8 3 32 N 4 24 N

A massive horizontal platform is moving horizontally with a constant acceleration of 10 m s as shown in the figure A particle P of mass m 1 kg is kept at rest at the smooth surface as shown in the figure The particle is hinged at O with the help of a massless rod OP of length 0 9 m Hinge O is fixed on the platform and the rod can freely rotate about point O Now the particle P is imparted a velocity in the opposite direction of the platform s acceleration such that it is just able to complete the circular motion about point O Then the maximum tension appearing in the rod during the motion is 10n Find the value of n J Joms 10 m s

In figure a smooth track which has a circular part of radius of curvature 0 1 m is shown The minimum height from where a small ball must be released from rest so that it completes the circle without leaving contact with the track is 1 Question Type Single Correct Type 2 3 0 1 m 0 2 m h 0 25 m R Re lew

o its axis If 0 3 T then d 0 44 N wire carrying of 45 with of 0 20 T is b 4 times d 16 times c 2 times 17 An electron of energy 1800 eV describes a circular path in magnetic field of flux density 0 4 T The radius of path is q 1 6 x 10 C m 9 1 x 10 kg a 2 58 x 10m b 3 58 x 10 m c 2 58 x 10 m d 3 58 x 10 m 18 Two

A proton is performing circular motion with radius 0 5 m under effect of normal magnetic field 1 Telsa Kinetic energy of proton is O 11 97 MeV O 13 27 MeV O 12 21 MeV O 8 39 MeV Marks 4 1

When a cyclist takes turn on a level road with constant speed A Net friction on him may be along tangential direction B Net friction on him may be along outward radial direction C Net reaction from ground should pass through center of mass of cyclist D Net reaction from ground may not pass from center of mass of cyclist

1 V 3 A small sphere is tied to one end and the other end is tied to a fixed support The sphere is released from rest keeping the string horizontal and straight so that the sphere moves in a circular path in vertical plane The angle that the string makes with vertical at which vertical component of tension force of string becomes equal to weight of the sphere is 1 45 3 tan 2 2 tan 2 3 4 cot a circular

The acceleration of a particle depend on displacement as a S 5 it is given that initially S 0 and V 5m s Q Find the relation between S and t A t log B C t loge 10 s 5 S 55

Consider a car moving on a horizontal road convex bridge and concave bridge of same radius R The speed of the car in each situation is same and equal to v the mass of the car is m then A me B C

A sphere of radius 0 1m and mass 8 kg is attached to the lower end of a steel wire of length 5m and diameter 10 m The wire is suspended from 5 22m high ceiling of the room When the sphere is made to swing as a simple pendulum it just grazes the floor at its lowest point The velocity of the sphere at the lowest position is m s Y for steel 1 994 10 N m A steel wire of diameter 0 8 mm and length 1m is clamped firmly at two points A and B which are 1m apart and in the same plane A body is hung from the middle point of the wire such that the middle point sags 1 cm lower from the original position The mass of the body is gm Young s modulus of the material of wire is 2 10 N m

13 A wheel starts from rest and attains an angular velocity of 20 radian s after being uniformly accelerated for 10 s The total angle in radian through which it has turned in 10 second is 1 20 2 40 3 100 4 100 t

Question 05 a A stone of mass m is rotated in a circular path with uniform speed by lying a strong string with the help of your hand Answer the following questions i Is the stone moving with uniform or variable speed ii Is the stone moving with a uniform acceleration In which direction does the acceleration act 3 iii What kind of force acts on the hand and state its direction b A boy of mass 30kg is sitting at a distance of 2m from the middle of the see saw Where should a man of mass 40 kg sit so as to balance the see saw c 1 Why is a long spanner is used to loosen a tight nut 2 2

From Eqs 1 and 2 we get Ti umg maj From Eqs 3 and 4 we get Mg 4T Maz Eliminating Ti from Eqs 6 and 7 and putting a 4a2 we obtain M 4 m M 16m 32 6 A flexible drive belt runs over a frictionless pulley as shown in figure The pulley is rotating freely about the vertical axis passing through the centre O of the pulley The vertical axis is fixed on the horizontal smooth surface The mass per unit length of the drive belt is 1 kg m and the tension in the drive belt 8 N The speed of the drive belt is 2 m s Find the net

In a park there are three concentric circular running tracks Radius of 2nd track is double of first and of 3rd track is triple of first Three runners are running on these tracks with constant speed When the runner in the first track completes one round the runner in 2nd has completed half round and the runner in third track has completed quarter round If the accelerations of the runners are in ratio a B y where a y are least integers then find the value of a B y 3

A thin slice is cut out of a glass cylinder along a plane parallel to its axis The slice is placed on a flat glass plate as shown The observed interference fringes from this combination shall be O straight O circular O equally spaced O having fringe spacing which increases as we go outwards 4

MCQ Single Correct Answer In the middle of the depletion layer of reverse biased p n junction the A electric field is zero B potential is maximum O electric field is maximum

Starting at the same moment and shown in the figure two cars are entering a turn with car A following the path a a and car B following the path b b The street is flat and level there is no banking or incline to the roadway For both of the cars the normal acceleration of 6 87 m s2 limits the constant speed of both cars What is the ratio of time t t it takes for the two cars to negotiate the turn as shown in the figure a b Finish Line 4 I T 1 88 m I 72 m

Shown in Fig Q4 a boat travels around a circular path r 40 m at a speed that increases with time v 0 0625 t2 m s Find the magnitudes of the boat s velocity and acceleration at the instant t 10 sec 20 points 40 m Fig Q4 v 0 06251

A roller coaster is moving as shown in figure It just completes the vertical circular motion on a path of radius 2m What should be the velocity at the highest point h 1 Question Type Single Correct Type 10g m s 2 5g m s 08 3 2g m s R 2m

3 14 A designer of race track is appointed on moon for a car race He has to design a 1 5 km diameter circular race track assuming a speed of 240 km hr for the type of cars used If everything else is to stay the same in the design by how many degrees and in which direction with respect to the horizontal designers will have to change the angle at which the track is banked on the moon as compared to the banking angle on earth The acceleration of gravity on the moon is 1 62 m s Ans Increase by 44 5 th A

3 15 The kinetic energy of a particle moving along a circle of radius r depends on distance covered s as K As where A is a constant Find the force acting on the particle as a function of s Ans 2As 1 s r 1

A uniform rod of mass m and length 3r is free to rotate about a horizontal axis through O A disc of mass m radius r is free to rotate about another horizontal axis fixed to other end of the rod say C r 1 2 m The system is released from rest when rod is horizontal What is the velocity of particle at A in m s when rod becomes vertical m 3r m

When a cylindrical vessel containing some liquid is rotated about its vertical axis the liquid surface is depressed drown at the axis of its rotation and rises up near the walls of the vessel on all sides This type of flow is known as Go for a cha Theater an art bir gun an A site act fant start an fache tue and as an ad at a steady flow b turbulent flow vortex flow TIE 2

A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed If the stone makes 22 revolutions in 44 s what is the magnitude and direction of acceleration of the stone AIPMT Prelims 2005 1 ms 2 and direction along the radius towards 4 the centre 2 ms 2 and direction along the radius away from centre 3 ms and direction along the radius towards the centre 4 ms 2 and direction along the tangent to the circla

A weightless thread can bear tension upto 3 7 kg wt A stone of mass 500 gms is tied to it and revolved in a circular path of radius 4 m in a vertical plane If g 10 ms then the maximum angular velocity of the stone will be 1 4 radians sec 2 16 radians sec 3 21 radians sec 4 2 radians sec that should be given

One end of string of length 1 is connected to a particle of mass m and the other end is connected to a small peg on a smooth horizontal table If the particle moves in circle with speed v the net force on the particle directed NEET 2017 towards centre will be T represents the tension in the string 1 T my 1 2 T 1 mv 1 3 zero 4 T h as shown in the figure just completes

A particle of mass m is moving in an uniform circular motion The momentum of the particle is 1 Constant over the entire path 2 Constantly changes and direction of change is along the tangent 3 Constantly chages and direction of chage is along the radial direction 4 Constantly chages and direction of change is along a direction which is the instantaneous vector sum of the radial and tangential direction circle with the other end of the string as the centre At

A coin placed on a rotating turntable just slips if it is placed at a distance of 4 cm from the centre If the angular velo of the turntable is doubled it will just slip at a distance of 1 1 cm 2 2 cm 3 4 cm 4 8 cm