Circular Motion Questions and Answers

13 Which relation is not correct of the following A Torque Moment of inertia x angular acceleration B Torque Dipole moment x magnetic induction C Moment of inertia Torque x angular acceleration D Angular momentum Moment of inertia x angular velocity H

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m s A plumb bob is suspended from the roof of the car by a light rigid rod of length 1 m The angle made by the rod with the track is a zero b 30 c 45 d 60

A disc of mass 3 kg and radius of 7 cm is placed on a rigid parabolic path x 4y at position 2 1 as shown It starts from this point at t 0 If friction is sufficient for pure rolling of the disc Then take g 9 8 m s and 2 1 4 A Velocity of disc at the position 0 0 is 9 8 15 m s 2 m 1 m 2 B Angular velocity of disc at 0 0 is 140 rad s 15 C Normal reaction at bottom point of the path is 49 N approx D Normal reaction at bottom point of the path is 98 N opprox 0 m 0 m

Figure shows a square current carrying loop ABCD of side 10 cm and current i 10A The magnetic moment M of the loop is A 0 05 i 3k A m B C 0 05 3i k A m D 0 05 j k A m i k A m B A 030 C i 10 D

What do the sunrise and sunset angles tell you about the length of daylight and night from place to plac over the course of the year 3 points tituds

A pipe is rotating with a constant angular velocity in a horizontal plane at a height of from the ground and completely filled with liquid of density p as shown in the figure One end of pipe is open and its cross sectional area is A At t 0 a hole of cross sectional area a a A is created on the other end Take atmospheric pressure P and take gl wl P Q R S Code A B List l The magnitude of flow velocity just outside the hole with respect to ground at t 0 The magnitude of flow velocity just outside the hole with respect to end point P of the pipe at t 0 The magnitude of velocity by which it collide with the ground first time The magnitude of velocity by which it collide with the ground first time with respect to end point P of the pipe P 4 4 Q 330 RI23 S231 Open A 1 2 3 4 List Il wl 200l 2wl l

A car moves with constant tangential acceleration at 0 80 m s along a horizontal surface circumscribing a circle of radius R 40m The coefficient of sliding friction between the wheels of the car and the surface is 0 20 What distance will the car ride without sliding if its initial velocity is zero

A motorcycle rider in the death well show in a circus is 17 67 m revolving along a circular path of radius r on the wall of the well If the coefficient of friction between the wall and the tyres of the motorcycle is then what minimum velocity should be maintained by the rider rg

A car starts from rest with a constant tangential acceleration a in a circular path of radius r At time to the car skids find the value of coefficient of friction

29 A balll is projected with 20 2 m s at angle 459 with horizontal the angular velocity of the particle at highest point of its journey about point of projection is 1 0 1 rad s 3 0 3 rad s 2 0 2 rad s 4 0 4 rad s

The block of mass M is connected by thread which is wound on a pulley free to rotate about fixed horizontal axis as shown A uniform magnetic field B exists in a horizontal plane The disc is connected with the resistance R as shown Calculate the terminal velocity of the block if it was released from rest Treat pulley as uniform metallic disc of radius L A B C 4mgR B L 2mgR B L D 3mgR 4B L 3mgR 2B L2 X X X X X X X X X X X X X X w R X X X X X B X X X X X XX X X X X X X M

To measure the moment of inertia of a wheel shaft system a tape of negligible mass is wrapped around the shaft and pulled with a known constant force F as shown in the figure When a length lo of the tape has unwound the system has an angular speed wo If the moment of inertia I of the wheel shaft system about an axis through C is equal to mR K Then find the value of K take lo 2R r R 2 F mR 9 R H 0

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

direction on A point P moves in counter clockwise a circular path as shown in the figure The movement of P is such that it sweeps out a length s 5 where s is in metres and it is im seconds The radius of the path is 20 m The acceleration of P when t 2 s is nearly AIEEE 2010 1 14 m s B 20 m P x y A 2 13 m s

b Part b refers to the figure below In part a you should have found that the time it takes the Moon to go around the Earth is about 27 days For this problem we will take the orbital period of the Moon to be TM 27 days While the Moon is orbiting around the Earth the Earth is also spinning on its axis The rotational period for the Earth to spin on its axis is TE 1 day In the figure below at t 0 we first show a person on the Earth directly opposite the Moon At t 12 hrs day the Earth did a half rotation and the Moon moved along its orbit At t 24 hrs 1 day the Earth did a full rotation and the 24 hrs Moon moved along its orbit Notice the person is not directly opposite the Moon at t 1 day since the Moon moved on its orbit At the time t the person is directly opposite the Moon again What is the time t for the person to be opposite the Moon again Hints Notice that at the time t the angle is the same for the person on the Earth and the Moon Thus we can use the equation OE OM to find t In this equation 0g is the angle the Earth makes and M is the angle the Moon makes Since the Earth and the Moon are rotating at constant speeds 0 wt where w 27 T Lastly when writing the equation OE OM you need to take into account that the Earth has done one full rotation and then the Earth rotates an angle 0 The angle for one full rotation in radians is the angle of a circle 27 You should find t to be close to 24 hours and 50 minutes This calculation shows us that the high tide on a place on the Earth occurs 50 minutes later the next day t 0 t 12 hrs or 1 t ONE 2 day Part b t 24 hrs or t 1 day t

A cylindrical wire of radius R is carrying current i uniformly distributed over its cross section If a circular loop of radius r is taken as amperian loop then the variation value of B di over this loop with radius r of loop will be best represented by A B di C fB dr R R B B de fB di Apsv R R

A particle of mass m connected to a string of length T then find out the tension in the string at the instant it is vertical if the particle is projected horizontally with a speed v 3gl from the bottom most point 2 3mg 4 5mg 1 2mg 3 4mg

66 A particle suspended by a light inextensible thread of length I is projected horizontally from its lowest position with velocity 7gl 2 The string will slack after swinging through an angle equal to a 30 b 90 c 120 d 150

X 1 A disc rotates about a fixed axis Its angular velocity o varies with time according to the equation at b Initially at t 0 its angular velocity is 1 0 rad s and angular position is 2 rad at the instant t angular velocity is 5 0 rad s Determine angular position 0 and angular acceleration a when 2 4 s

4 ROWS The following table has 3 columns and 4 rows Based on table there are THREE questions Each question has FOUR options A B C and D ONLY ONE of these four options is correct Column l shows four situations with a small ball of mass m connected to an ideal string of length I and fastened to a point O whose acceleration if any is shown in the diagram Column ll lists the minimum value of speed u with respect to point of suspension when the string is vertical in order for the mass to complete the circular motion in vertical plane Column III lists the maximum tension throughout the circular motion corresponding to minimum speed Column 1 Column 2 Column 3 e 1 11 111 IV O 19 3 l l l 45 g 3 u 2g u i ii 3ge iv 2ge 3 1 iii 5gl 20 gl 3 P 6 mg Q 4 3 mg R 7 mg 37 S 8 mg

1 162 6 N 3 42 7 N 34 A block is projected with speed 20 m s on a rough horizontal surface The coefficient of friction between the surfaces varies with time t as shown in figure The speed of body at the end of 4 second 0 0 5 0 3 1 2 m s 72 m s To 2 89 7 N 4 95 2 N 2 4 t s 2 5 m s 4 9 5 m s 09 tim a smooth inclined plane o and height h If same b rough inclined plane of s and same height and tak value then coefficient t inclined plane is 1 1 n tan 0 3 1 n tan 0 39 If acceleration of acceleration of B applied by B on

Aparticle is travelling in a circular path of radius 4m At a certain instant the particle is moving at 20m and its acceleration is at an angle of 37 from the direction to the centre of the circle as seen from t particle 1 At what rate is the speed of the particle increasing ii What is the magnitude of the acceleration

A particle moves in a straight line under an acceleration varying linearly with time Its velocity time graph is shown in figure Then v m s 37 45 01 t s 1 The particle comes to rest at t 7 s 2 The initial velocity of particle is 1 m s 3 Maximum velocity of particle is 2 m s

Physics Calculate the following for the situation shown Speed at D Normal reaction at D Height H Fris H 265 B of static friction between

In the given figure O is the centre of regular pentagon ABCDE Five forces each of magnitude Fo are acted as shown in figure The resultant force is a 5 b SF cos 72 c 5F sin 72 d zero Fa C F

Illustration 5 73 A stone tied to an inextensible string of length 1 1 m is kept horizontal If it is released find the angular speed of the stone when the string makes an angle 0 30 with horizontal

8 Two simple pendulums of length 5 m and 20 m respectively are given small linear displacements in one direction at the same time They will again be in the same phase when the pendulum of oscillations shorter length has completed 1 2 3 5 2 1 4 3

A zero resistance coil of inductance L connects the upper ends of two vertical parallel long conductors A horizontal sliding conductor free to slide up and down always maintaining contact with the vertical conductors starts falling from rest at t 0 due to its own weight mg A uniform magnetic field of magnitude B exists in the region horizontally and perpendicular to the plane of the conductors The distance between the vertical conductors is l After what time does the conductor come back to its starting position Also find maximum speed achieved

Q14 A point mass m is suspended from a light thread of length fixed at O is whirled in a horizontal circle at constant speed as shown From your point of view stationary with respect to the mass the forces on the mass are A F W m B m C m D F T 111

Height H A car is moving along a hilly road as shown side view The coefficient of static friction between the tyres the pavement is constant and the car maintains a steady speed If at one of the points shown the driver ap brakes as hard as possible without making the tyres slip the magnitude of the frictional force immedi after the brakes are applied will be maximum if the car was at A B C D point A point B point C friction force same for positions A B and C A B ircular path in a vertical

A material particle of mass m is revolving along a hor izontal circular path of radius r under the influence of the centripetal force k constant What will be x the total kinetic energy of the particle k 2r k

Two men A and B are sitting at the end of a plank of length L if plank is rotating with angular velocity about an axis perpendicular to its length and passing through a point at a distance of L 3 from A The angular A velocity of B with respect to A is A C 20 3 B L 3 D 2 L 3 3

urvature is 40 m The outer edge is above the lower edge by a distance of 1 28 m Find the velocity of vehicle for which the road is most suited g 10 m s A stone of mass 1 kg tied to a light string of length 10 m is whirling in a circular path in the vertical plane If the ratio of the maximum to minimum tensions in the string is 3 find the speeds of the stone at the lowest and highest points 55

Fig 10 Two point masses m are connected the light rod of length I and it is free to rotate in vertical plane as shown in Fig 8 154 Calculate the minimum horizontal velocity is given to mass so that it completes the circular motion in vertical lane Fig

Consider the shown diagram where the two chambers separated by piston spring arrangement contain equal amounts of certain ideal gas Initially when the temperatures of the gas in both the chambers are kept at 300 K The compression in the spring is 1 m The temperature of the left and the right chambers are now raised to 400 K and 500 K respectively If the pistons are free to slide the final compression in the spring in cm is 10 x Find value of x 300K 1m 00000000 Vacuum 300K Im

Find acceleration of CM and angular acceleration of cylinder while acceleration of points A B are a aoi and ap ao j 1 0 ao R aof 2a0 B A ao 2 ao 0 4 None of these

Comprehension I A pendulum bob has mass m The length of pendulum is t It is initially at rest A particle P of mass m 2 moving horizontally along ve x direction with velocity 2ge collides with the bob and comes to rest When the bob comes to rest momentarily another particle Q of mass m moving horizontally along z direction collides with the bob and sticks to it It is observed that the bob now moves along a horizontal circle The floor is a horizontal surface at a distance 2 below the point of suspension of the pendulum 1 Tension in string immediately after the first collision is A 2mg B mg 3 5 C 99 201 mg 2 D mg 20 12

4 1 1 m disc of radius R and mass M can rotate without friction on an axle passing u through its centre and perpendicular to its plane face A cord is wound over the rim of the disc and a uniform force F is applied on the cord as shown in the adjoining figure Then the tangential acceleration of a point on the rim of the disc is proportional to OR ft F fue V

A rod OA of mass m and length L hinged at end O can rotate smoothly in vertical plane about horizontal axis passing through O It is released from a horizontal position as shown in the figure and strikes a block of mass M kept vertically below O at distance L on a smooth horizontal surface The block after collision moves on the smooth vertical circular B track of diameter L such that the force exerted by the circular track on the block at third of its weight If the rod after collision rotates through an angle 30 from the he ratio of masses M m A 30 M

16 In a machine a horizontal arm of 2 m is connected with a vertical shaft and is rotated at an angular velocity of 600 rpm in a horizontal plane A 10 kg block is attached to the free end of the arm Find out the force on the block and the force on the vertical shaft due to rotation of the block 78957 N 78957 N

A Bob of mass m is attached to a massless string whose other end is connected to the fixed support O Initially string is horizontal and bob is held at rest At t 0 bob is released and it takes time t to reach bottom most position During the given interval of time t R A Average value of tension in string is m g 1 B Average value of tension in string is mg e Magnitude of angular momentum of bob about point O will increase D Average value of torque due to weight of bob about O will be m 2gR R t ox

A circular disc of radius r is rotating with a constant angular velocity e in a vertical place about a fixed horizontal axis passing through its centre O At the time t 0 a particle flies off the disc from the point A on the disc as shown After some time it again sticks to the disc at the same point A Assuming the mass of the particle to be negligible small the value of 0 is A cos 8 TO the B cos C sin 3 YEAR 170 D sin

A particle is rotating about a vertical axis in the horizontal plane such that the angular velocity of the particle about the axis is constant and is equal to 1 rad s Distance of the particle from axis is given by R Ro t where t stands for time The speed of the particle as a function of time is A 1 c B R Bt B R Bt D B R

The distance of a particle moving on a circle of radius 12 m measured from a fixed point on the circle and measure along the circle is given by s 2t in meters The ratio of its tangential to centripetal acceleration at t 2s i 1 1 1 3 2 1 2 1 2 4 3 1

9 T mwa me4u 2 2 Two blocks each of mass 5 kg are the ends of a light rod as shown in the figure 5kg in 14Ha 566 5x1x4X172 100 5kg 1 m 120X The rod is rotated about a vertical line of symmetry The r d breaks if the tension in i exceeds 500 N The maximum frequency L rotation per second with which the rod may b without breaking is

A block of mass m is constrained to move inside a ring of radius R which is fixed on a horizontal smooth table At time t 0 block is moving along the inside of the ring i e in the tangential direction with velocity vo The coefficient of friction between the block and the ring is u Then the speed of the block at time t is 1 Vo R vot 2 Vo vot 1

Ap 2mu sin Uj i Radius of curvature at the point of projection when direction of motion or velocity is a with the v u cos 0 g cos a horizontal is P At the highest point p g cos a u cos 0 g where v is instantaneous velocity and u is initial velocity minimum

ne speed of a boat is 5 km hr in still water It crosses a river of width 1 km along the shortest passible path in 15 minutes The velocity of river water is 1 3 km h 2 4 km h 3 5 km h 4 2 km h

A man is moving on a circular path of radius R on horizontal ground with constant angular velocity o Rain is falling with constant velocity 4 ms making an angle 45 with vertical in the plane containing north south direction Find the magnitude of average velocity of rain with respect to man in one full rotation

A uniform disc of mass m and radius R is resting on a table on its tim The coefficient of friction between disc and tabte is u The disc is pulled horizontally from its central axis with a force F What is maximu value of F for which disc rolls without FOL Limited F 2 3 mg