Circular Motion Questions and Answers

point on the circumference of a wheel of radius R 1 3 m The other end is sliding freely along a straight channel passing through the center O of the wheel as shown in the figure below The wheel is rotating with a constant angular velocity o about O a R Co 2 c The speed of the sliding end P when 0 60 is 200 3 L 200 b J 300 a P 3

D A cyclist speeding at 5 m s on a level road takes a sharp circular turn of radius 2 5 m without reducing the speed The minimum value of coefficient of static friction between tyre and road such that cyclist does not slip is NCERT I XI Pg 105 1 0 5 2 1 5 3 1 0 4 0 8 truck startar from

34 On a pulley of mass M hangs a rope with two masses m and m m m tied at the ends as shown in the figure The pulley rotates without any friction whereas the friction between the rope and the pulley is large enough to prevent any slipping Which of the following plots best represents the difference between the tensions in the rope on the two sides of the pulley as a function of the mass of the pulley a c 1 1 T m M M M T m b d M M

ALLEN 74 The relay satellite transmits the television 78 programme continuously from one part of the world to another because its 1 Period is greater than the period of rotation of the earth about its axis 2 Period is less than the period of rotation of the earth about its axis 3 Period is equal to the period of rotation of the earth about its axis 79

2 140 The radial position of a fluid particle P in a certain centrifugal pump with radial vanes is approxi mated by r ro cosh Kt where t is time and K 0 is the constant angular rate at which the impeller turns Determine the expression for the magnitude of the total acceleration of the particle just prior to leaving the vane in terms of ro R and K R P 0 Fixed reference axis

The two ends of an inextensible string of length and mass m are fastened together on a circular loop and set spinning about the centre of the circle with a uniform angular velocity w The tension in the string is a mw b mw 1 2 c mw d mw 1 4

A point mass m is moved in a vertical circle of radius r with the help of a string The velocity of the mass is 7gr at the lowest point The tension in the string at the lowest point is 1 6 mg 2 7 mg V 8 mg 4 1 mg

A cylindrical body of radius R is kept stationary on a flat horizontal surface A rod leans against the body inclined at an angle 0 with the horizontal The left end of the rod slides to the left on the floor with a constant velocity v The angular speed of the rod is VE vR 1 S 3 vR 0 KS 2 R VS R KS

A cylinder of mass m and radius R rolls purely over an inclined surface while moving up on it Correct statement regarding friction acting on it is 1 Friction is acting downward and Kinetic in nature 2 Friction is acting upward and kinetic in nature 3 Friction is acting upward and static in nature 4 Friction is acting downward and static in

LA solid sphere of radius R is placed at rest on a rough horizontal surface The sphere is given a horizontal impulse at a height habove its lowest point Consequently it starts rolling without slipping The value of his 1 R 2p A 2 T h 5 3 7 R

12 A particle of mass m is moving in a of fixed radius r such that its centripeta acceleration a is varying with time as a k rt2 where k is constant The power delivered to the particle by the forces acting on it as a function c time t is 1 2rmk r t 1 2 mk r t 3 path n

5 A particle of mass 4 kg is moving on x y plane with velocity v 10 m s The position vector of particle at an instant t is 7 51 81 m Find the angular momentum of the particle at this instant about the origin 1 250 k Js 2 2 320 k Js

35 Two balls A and B are thrown with speeds u and u 2 respectively Both the balls cover the same horizontal distance before returning to the plane of projection If the angle of projection of ball B is 15 with the horizontal then the angle of projection of A is 36 1 sin 3 sin col 8 100 8 2 sin 8 KN0136 what angle the horizontal should a

A uniform disk of radius 4 m is moving in x y plane with its centre on x axis having constant positive velocity 5 m s along x axis and constant angular velocity 10 rad sec Taking the centre of disc as origin find out the magnitude of velocity of point A 3 0 with respect to point B 1 3 both lying on the disc

My bicycle has a 26 0 inch 66 0 cm diameter tire If my bike is moving at 12 mi hr 5 36 m s how long does it take the tire to go around once How many rpm s

When a particle moves at constant speed v in a circle or a circular arc of radius r the acceleration of the particle is directed 1 the centre of the circle and has a constant magnitude ii 1 towards away from 112 v CTS

4 For an object traveling with uniform circular motion its acceleration is a zero because the speed is constant b directed tangent to the circle c directed toward the center of the circle d changing in magnitude depending on its position in the circle e directed outward from the center of the circle 5 An object moves with a speed of 2 4 m s in a circle of radius 1 6 m Its centripetal acceleration a 9 2 m s b 7 4 m s c 3 6 m s d 1 5 m s e 0 94 m s 6 When analyzing dynamics problems free body diagrams a should always be used b are more useful when analyzing horizontal forces than when analyzing vertical forces c should include only the forces that are directly responsible for the acceleration d should be used only when objects are accelerating e only apply to objects in equilibrium

126 Ray Optics and Optical Instruments 19 Biconvex lenses are to be manufactured from glass of refractive index 1 5 with both faces of same radii of curvature The radius of curvature required if focal length is 15 cm will be

A beam of neutrons performs circular motion of radius r 1 m under the influence of an inhomogeneous magnetic field with inhomogeneity extending over Ar 0 01 m The speed of the neutrons is 54 m s The mass and magnetic moment of the neutrons respectively are 1 67 10 7 kg and 9 67 x 10 27 J T The average variation of the magnetic field over Aris approximately KVPY SX 2020 1 0 5 T 3 5 0 T 2 1 0 T 4 10 0 T

The acceleration of a cart started at t 0 varies with time as shown in figure Find the distance travelled in 30 seconds Options 100 fts 3000 fts 1000 fts Acceleration in ft s 5 0 5 0 10 20 30 Time in second

Question No 105 For a particle in motion in a plane if the angle between the velocity vector and acceleration vector is a right angle always then the particle A is speeding up along its path B is slowing down along its path C may be speeding up or slowing down D is neither speeding up nor slowing down 3 A B C D 10 10 11

For a particle in motion in a plane if the angle between the velocity vector and acceleration vector is a right ang always then the particle A is speeding up along its path B is slowing down along its path C may be speeding up or slowing down D is neither speeding up nor slowing down A B

eed 5 R orbit orbit 45 If the magnitude of gravitational pote ergy of a system is varies according to the relation SUG Ux then time period of revolution is le beega orll 2 beonario al rinse erit to du In joven Mevloven lliw S Mioven lin 11 proportional to 1 3 2 to fidio 2 2 tido 3 4 ro 2010

4 A particle is revolving in a circular path of radius 2 m with constant angular speed 4 rad s The angular acceleratio of particle is 1 Zoro 3 16m rad s 2 4 8 rad s 128m rad s

24 A circular ring of mass M and radius R lies on a smooth horizontal surface An insect of mass m starts moving round the ring with uniform velocity v relative to the ring Choose the correct option s Use M m R M V A Angular velocity of ring with respect to the ground is 3R C Speed of insect with respect to the ground is Om V B Angular velocity of ring with respect to the ground is 2R Speed of insect with respect to the ground is 3 C DHYSICS VIR VS VR MR MR V MR2 MR V MR 7 MR N

61 A particle is projected horizontaily at the top of a smooth hemispherical bowl at point A The particle leaves contact with the surface at point B 1 4 for which 0 sin as shown Speed of projection of the particle equals radius of the bowl 40 cm and take g 10 m s 1 0 25 m s 3 YA Ai B Smooth hemispherical bowl fixed to ground X 2 0 5 m s

A block of mass m slides on a circular track of radius r whose wall and floor both have coefficient of kinetic friction u with the block The size of block is small compared to the radius of the track The floor lies in horizontal plane and the wall is vertical The block is in contact with both wall and the floor The block has initial speed vo along tangent of circular track For the block to circle the track exactly once before coming to rest initial velocity vo needed is A B C D rg e rg 4 x rg 2 LUXE rg 2 m 041

A particle moving with velocity i 31 produces an electric field E 2k at some point It will produce a magnetic field at that point which is equa 0 A B 61 2j c Correct Answer 6i 2j c zero ifician

A small block with a mass of 150 gm slides without friction along a semicircular wire with a radius of 8 cm that rotates about a vertica axis at a rate of 2 revolutions per second as shown in the figure The maximum value of 0 for which the block will remain stationary w r t the rotating wire is Oo find value of sec Bo Take m 10 8em

The kinetic energy of a particle moving along a circle of radius 1 m depends on the distance covered d as K bd2 where b is a constant Find the force acting on the particle when the particle has covered 3m distance O 4b 3N O 2b 3N O 3b 3N

4 6 25 1 m s radius 1m varies with time as v 2t Here v and t d of a particle moving in a circular path of are measured in SI units Find acceleration of particle at t 1s 1 2 2m s 2 4 2m s 3 4 m s 2 m s2

20 A ball is moving in a circular path of radius 5 m If tangential acceleration at an instant is 10 m s 2 and the net acceleration makes an angle 30 with the centripetal acceleration then the instantaneous speed is 1 50 3 ms 1 3 6 6 ms 1 2 9 3 ms 1 1 26

Bob B of the pendulum AB is given an initial velocity 3Lg in horizontal direction Find the maximum height of the bob from the starting point if AB is a massless rod OL 2 T L B

In the figure one fourth part of uniform disc of radius R is shown The distance of the centre of mass of this object from centre C 995 O 4R 3A O 2R 3m 4R IN 5 90 R

A wheel undergoes a constant angular acceleration from time t 0 to t 20 s and thereafter angular acceleration is zero If angular velocity at t 2 s is found to be 5 rad s then the number of revolutions made by the wheel in time interval t 0 s to t 50 s is

two identical spheres of mass m and charge q are you suspended from a common point by two of same length I and it is found that threads make an angle Theta with vertical when sphere are in equilibrium calculate the value of q PLEASE A SOLVE THE PROBLEM IN PAPER

5 14 A straight conducting wire PQ of length is fixed along a diameter of a non conducting ring as shown in the figure 5 285 The ring is given a pure rolling motion on a horizontal surface such that its centre of mass has a velocity v There exists a uniform horizontal magnetic field B in horizontal direction perpendicular to the plane of ring The magnitude of induced EMF in the wire PQ at the position shown in the figure will be A Bvl C 3Bvl 2 X X X B 2 Figure 5 285 X B 2Bvl D Zero

Full Marks Zero Marks Negative Marks 3 If only the correct answer is given 0 If no answer is given 1 In all other cases rope is hanging vertically with its two ends fixed to walls at same horizontal level as shown Tension at the bottom most point is 90 N If the mass unit length of ope is 4 kg m find radius of curvature in metres at point C Take g 10 m s 30

A light rod of length L is hanging from the vertical smooth wall of a vehicle moving with acceleration 3 g having a small mass attached at it s one end is free to rotate about an axis passing through the other end The minimum velocity given to the mass at it s equilibrium position so that it can complete vertical circular motion is KgL Find the value of K

An object comprises of a uniform ring of radius R and two small identical disc as shown Which of the following can not be the centre mass of the object O RR 3 3 O RRY 3 2 O R R O R R 21 n 1 ring disc

A circular disc of radius of gyration 20 cm at rest is dropped over another disc of same mass but double the radius of gyration rotating with 5 rad s If both the discs club together and rotate as one body about the same axis then the new combined angular speed of the discs is 1 1 rad s 2 2 rad s 4 4 rad s 3 3 rad s

9 De Broglie wavelength of two particles are in the ratio of 1 3 If a magnetic field is applied perpendicular to their velocity ratio of the radii of circular path described by them is 2 1 What is ratio of magnitude of charge on each 3 3 2 1 2 3 2 1 6 4 6 1

ALLEN Ball of mass m 0 5 kg is attached to the end of 5 a string having length L 0 5 m is rotated on a horizontal circular path about the vertical axis The maximum tension that the string can bear is 324 N What is the maximum possible value of angular velocity of ball in radian s m 1 9 3 27 A skater of mass m is standing on ice throws 2 18 4 36 m 0 5 kg faften L 0 5 na an 3324 Nu a ne RIT v f r ge 1 9 3 27 43 m 2 18 4 36 mer Afera fem

A ring of radius R is rolling purely on the outer surface of a pipe of radius 4R At some instant the center of the ring has a constant speed v Then the acceleration of the point of the ring which is in contact with the surface of the pipe B 3v 5R C v 4R D Zero is A 4v 5R

9 A car is moving rectilinearly on a horizontal path with acceleration a A person sitting inside the car observes that an insect S is crawling up the screen with an acceleration a If 0 is the inclination of the screen with the horizontal the acceleration of the insect a parallel to screen is a a cos 0 c perpendicular to screen is a sin 0 b along the horizontal is a a cose d perpendicular to screen is a tan 0

5 In the diagram shown the block placed on the rough horizontal plane is just in a state of rest If the particle is performing uniform circular motion with angular velocity on a circle of radius R then find out the coefficient of friction between the block and the horizontal surface A R g 2 1 2 B 2 R g 2 11 2 C 0 5 R g 1 2 D None The block has mass M and the particle has mass 2M

The bob of a pendulum has mass m 1kg and charge q 40 Length of pendulum is l 0 9 m The point of suspension also has the same charge 40 C The minimum speed u that should be imported to the bob so that it can complete vertical circle is in m s Take g 10m s

A small particle of mass 0 36 gm rests on a horizontal turntable at a distance 25 cm from the axis of spindle The turntable accelerated at a rate of a 1 3 rads The frictional force that the table exerts on the particle 2 sec after the startup is A 40 IN B 30 N C 50 HN D 60 N

A particle moves along the arc of a circle of radius R according to the equation a sin wt where is the length of path and a and w are constants Then the magnitude of the total acceleration of the particle at the point 0 will be a co R B C 2a 00 D None of these A a c0 2R

The angular displacement in radius of an accelerated flywheel is given by 0 92 The linear velocity of a point at distance 0 75 m from the axis of rotation at the instant when magnitude of its tangential acceleration normal acceleration are equal is equal to x m s Find value of x