Circular Motion Questions and Answers

16 Two uniform discs A and B of equal masses and different radii rA and TB are mounted on fixed horizontal axles passing through their centres On each of the discs a light inextensible long cord is wound and the discs are held motionless If free ends of both the cords are pulled with equal forces for equal amounts of time lengths of the cord unwound from the discs A and B bear the relation relation a lA IB a L 1 b lA IB d More information needed

3a below its A particle is moving with constant speed u inside a fixed smooth hemispherical bowl of radius a describes a horizontal circle at a distance 2 centre Then The radius of the circular motion is The value of u is ag 2 3 mg The normal reaction of the spherical surface on the particle is The magnitude of the resultant force acting on the particle is zero in an inertial frame

A merry go round rotates from rest with constant angular acceleration a Ratio of time to rotate first 2 revolutions and next 2 revolutions is 2 2 1 1 4 1 2 1 1 1 3 2 1

A block of mass m is at rest w r t disc and disc is rotating with angular velocity w and having angular acceleration a then which of the following is correct a O In inertial frame net force on the block is equal to friction force O Normal on block increases with time O Friction force will be towards centre Friction force on the block is not constant JJ

Figure shows a bob moving in horizontal circular motion at angular speed 21 find value of N Strings are of equal lengths and inextensible T tension in supporting strings T is given by 3 2g where AB h The ratio of

A cylinder with radius R spins about its horizontal axis with angular speed w There is a small block lying on the inner surface of the cylinder The coefficient of friction between the block and the cylinder is u Find the possible values of w for which the block remains at rest with respect to the cylinder Take R 1 m 0 2 AR 0

A particle is moving with constant speed u inside a fixed smooth hemispherical bowl of radius a describes a horizontal circle at a distance below its centre Then a The radius of the circular motion is 2 The value of u is ag 2 3 3a 2 The normal reaction of the spherical surface on mg the particle is 2 The magnitude of the resultant force acting on

A bullet of mass 50 g enters a block of thickness t with speed of 500 ms It emerges with 4 of its initial kinetic energy The emergent speed is 1 100 ms 1 2 200 ms 3 300 ms 1

In a non uniform circular motion of a particle Angular acceleration of perpendicular to acceleration of particle particle is Angular acceleration of perpendicular to velocity of particle particle is Angular velocity of particle is perpendicular to acceleration of particle Angular velocity of particle is perpendicular to velocity of particle

Figure 38 W14a shows a conducting circular loop of radius a placed in a uniform perpendicular magnetic field B A metal rod OA is pivoted at the centre O of the loop The other end A of the rod touches the loop The rod OA and the loop are resistanceless but a resistor having a resistance R is connected between 0 and a fixed point C on the loop The rod OA is made to rotate anticlockwise at a small but uniform angular speed a by an external force Find a the current in the resistance R and b the torque of the external force needed to keep the rod rotating with the constant angular elocity w A E Boa 2 X X R 240 0 Cx a 3 A X R OF HA b

A bird in air is diving vertically downward over a tank with speed 5 cm s while base of tank is silvered A fish in the tank is rising upward along the same line with speed 2 cm s water level is falling at rate of 2 cm s take water 4 3 L Speed of image of fish as seen by bird directly is 6 cm s B Speed of image of fish as seen by bird directly is 3 cm s Speed of image of fish as seen by bird after reflection from mirror is 3 cm s D Speed of image of fish as seen by bird after reflection from mirror is 6 cm s

W motor car is travelling at 60 m s on a circular road of radius 1200 m It is increasing its speed at the rate of 4 m Find the acceleration of the car is in m s

Quesuon No 6 For Example If first third and fourth are the ONLY three correct options for a question with second option being an incorrect option selecting only all the three correct optio in 4 marks Selecting only two of the three correct options e g the first and fourth options without selecting any incorrect option second option in this case will result Selecting only one of the three correct options either first or third or fourth option without selecting any incorrect option second option in this case will result in 1 marks incorrect option s second option in this case with or without selection of any correct option s will result in 1 marks A particle is moving in a circle of radius 2m with angular velocity w 2t2 4t where t is time in sec and wis in rad s Angular acceleration of the particle at t 2 sec is 4 rad s Angular acceleration of the particle at 2 sec is 8 m s Angular acceleration of the particle is constant 32 Angle rotated by particle in time interval t 0 to t 4 sec is 3 radian

You are shown a photo of a car driven on a vertical inside wall of a huge cylinder with a radius of 10 m The coefficient of static friction between the car tires and the cylinder is us 0 25 The minimum speed in m s at which the car can be driven like that is 5x Find x

A particle of mass m is moving with constant velocity vo along the line y b At time t 0 it was at the point 0 b At time t Angular momentum of particle about origin is 2mvob Angular momentum of particle about origin is having value equal to mvob Torque acting on particle about origin is zero Torque acting on particle about origin is Non zero

The three 200 g masses in figure are connected by massless rigid rods to form a triangle What is the triangle s rotational kineti energy in joule if it rotates at 3 rad s about an axis through the center 10cm 60 Axis 40cm 60 40cm

Angle 8 rotated by a particle in circle varies with time t as 0 2t 1 O Average angular velocity between t 0 to t 1 second is 1 rad sec Average angular velocity between t 0 to t 1 second is 2 rad sec Magnitude of angular acceleration at t 2 sec is 12 rad sec Particle changes its direction of angular velocity once after t 0

1 When a bob is suspended by a light string and it is imparted to a horizontal velocity to complete the full circular trajectory in a vertical plane What is the difference in tension between the lowest and highest point of the path 1 mg 315mg 26mg 4 3mg

A particle of mass 10 g moves along a circle of radius 6 4 cm with a constant tangential acceleration What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to 8 x 10 4 J by the end of the second revolution after the beginning of the NEET 2016 motion 1 0 2 m s 2 0 1 m s 3 0 15 m s 4 0 18 m s

13 In the diagram shown all the velocities are given with respect to earth What is the relative velocity of the image in mirror 1 with respect to the image in the mirror 2 The mirror 1 forms an angle with the vertical A 2v sin2 C 2v sin2 B 2vsin D None of these Mirror 1 I Object Mirror 2

A ball attached to an end of a string is released from horizontal position as shown For what value of angle between string and vertical during its motion the total acceleration is directed horizontally 90 O O O 90 sin

8 A solid cylinder of mass 2 kg and radius 4 cm is rotating about its axis at the rate of 3 rpm The torque required to stop after 2 revolutions is 3 a 2 x 10 N m c 2 x 106 N m b 12 x 10 4 N m d 2 x 10 6 N m

A proton moving with a speed of 3 0x105 m s perpendicular to a uniform magnetic field of 0 20 T will follow which of the paths described below qp 1 6x10 19 C and mp 1 67x10 27 kg a A straight line path b A circular path of 1 6 cm radius c A circular path of 3 1 cm radius d A circular path of 0 78 cm radius

A body revolves with constant speed v in a circular path of radius r The magnitude of its average acceleration during motion between two points in diametrically opposite direction is 12 1 Zero Vo 2v islenm 4 v

3 220 rad s 37 Centripetal acceleration of a cyclist completing 7 rounds in a minute along a circular track of radius a constant speed is 1 2 7 m s 3 3 78 m s2 2 4 m s 4 6 m s hinct in uniform circular motion is doubled its acceleration becomes

A bead of mass mis released from rest at point A and move along smooth circular track as shown in the figure The ratio of magnitude of centripetal force and normal reaction by track on the bead at any point B described by an angle 0 would in general O R Increase with 0 Decrease with e Remains constant 0 m B A First increases with 0 and then starts decreasing

A ball of mass m 0 5 kg is attached to the end of a string having length L 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 radian s is A 9 B 18 3 1 1 C 27 D 36

A particle moves along a circle of radius 10 cm If its linear speed changes from 4 m s to 5 m s in 1 s then its angular acceleration will be O O O 2 rad s 5 rad s 10 rad s

A particle attached to a light wire of length is projected horizontally with a velocity of 5ge Calculate its net acceleration when wire becomes horizontal 1 Zero 2 10g 3 g 4 3g

Moment of inertia of uniform circular disc about a diameter is Its moment of inortin about an axis perpendicular to its plane and passing through a point on its rim will be 415 5 2 31 3 6 4 4 tyt GMR 2 21

A body is revolving with a constant speed along a circle If its direction of motion is reversed but the speed remains the same then a the centripetal force will not suffer any change in magnitude b the centripetal force will have its direction reversed c the centripetal force will not suffer any change in direction d the centripetal force is doubled 1 a b 2 b c 3 c d 4 a c

0 A particle is moving on a circular path of radius 5 m with uniform speed 10 ms from point A to B The magnitude of average velocity of particle in moving from A to B is 1 2 ms 1 T 20 B O 2 A 10 T 1 ms 72 511

A particle of mass m moving with speed u collides with the plate of mass m and sticks to it as shown in figure The rectangular plate is free to rotate about an axis passing through the centre in horizontal plane After the collision the angular velocity of the plate will be a 2a

65 A rod of length 50 cm is pivoted at one end It is raised such that it makes an angle of 30 from the horizontal as shown and released from rest Its angular speed when it passes through the horizontal in rad s will be g 10 ms 30 2 1 2 3 3 30 30 30

A roller coaster loaded with passengers has a total mass of 2 77E 03 kg the radius of curvature of the track at the lowest point of the track is 25 8 m If the vehicle has a tangential speed of 18 6 m s at this point what force in kN is exerted on the vehicle by the track

Two identical charged spheres are suspended by strings of equal lengths The strings make an angle of 30 with each other When suspended in a liquid of density 0 8 g cm the angle remains the same If density of the material of the sphere is 1 6 g cm the dielectric constant of the liquid is a 1 b 4 c 3 d 2

3 Into a transverse uniform magnetic field of induction 6 5 G an electron is projected with a speed 4 8 x 10 m s at angle second is 90 to the boundary The time elapsed by the electron in the field in nano A 56 25 C 28 1 B 65 2 D infinity

A particle of mass m and charge q is projected with a velocity v perpendicular to a uniform magnetic field B Plot graphs showing the variation of the radius of the circular path traced b it with i increase in its charge ii increase in its KE where in each case the other factors remain constant

A point moves along a circle such that distance travelled S at where a m s and t is time 1 2 in second Find the total acceleration of the point at the moment when it covered the nth n 0 10 fraction of the circle after the beginning of the motion Take 10 A pulley block system inside lift is shown in figure The pulleys and the threads are ideal and

3 31 A large mass M and a small mass m hang at two string that passes through a smooth tube as shown in figure 3 89 The mass m moves around a circular path which lies in the horizontal plane The length of the string from the mass m to the top of the tube and 0 is the angle this length makes with the vertical The frequency of rotation of mass m so that mass M be stationary will be 1 Mg A 2 ml V C 1 mg 2 V M Horizontal Plane Tube M Figure 3 89 B 0 D String ml 2 Mg 1 mM 2 V gl

42 zu A hemispherical bowl of radius R is set rotating about its axis of symmetry which is kept vertical A small block kept in the bowl rotates with the bowl without slipping on its surface If the surface is smooth and the angle made by the radius through the block with the vertical is 0 find the angular speed at which the bowl is rotating 1 3 Lak R g Rsine VRT 4 g Rcose g Rtane 26 1 2At Las 4 A particle moves in the x influence of a force such th is p t i cos at jsin are constants The angle the momentum is 27 TCV 3At 1 0 Apre 60 Figure shows plot of fo during the collision of a initial velocity of the ball is

A particle is moving in a circle of radius m and mass of the particle is 2 kg The kinetic energy 2 m 3 of the particle depends on distance S travelled by the particle as K E 4S The angle made by net acceleration with the radial acceleration when the particle rotate by 60 is 3 A tan 6 B tan TC C tan TC D tan 1 TC TC

A disc is given angular velocity as shown in figure and kept on an inclined plane of inclination having coefficient of friction tan 0 The initial acceleration of centre of mass is a and angular acceleration a then aR a 2aR a aR gsin 0

3 98 An insect crawls up a hemispherical surface very slowly see the figure 3 114 The coefficient of friction between the insect and the surface is 1 3 If the line joining the centre of the hemispherical surface to the insect makes an angle a with the vertical the maximum possible value of a is given by A cot a 3 C sec a 3 Figure 3 114 B tan a 3 D cosec a 3

A point mass moves along a circle of radius R with a constant angular acceleration a How much time is needed after motion begins for the radial acceleration of the point mass to be equal to its tangential acceleration

A particle of mass 1 kg is tied with an inextensible string of length 1 m in the vertical plane as shown in the figure At lowest point a horizontal velocity of 40 m s is imparted to particle XX represents a horizontal level passing through the point of suspension X A 40 m s The speed of particle at instant when tension in the string becomes zero is B C m D 20 10 3 5 2013 0 40 3 m s m s m s m s

Arace car travels around a horizontal circular track that has a radius of 100m If the car increases its speed at a constant rate of 2m s The time needed for the car to reach an acceleration of 3m s is

A 5 68 A particle is revolving in a circular path as shown in figure in the horizontal plane such that the angular velocity of the particle about the point O is constant and equal to 1 rad s Distance of the particle from O is given by R R Bt where R C and are constant The speed of the particle as a function of time is A B 1 C Ro B1 hao C Figure 5 122 R B R Bt D B 81 2 5 7 roll of

A track is tangent to a circular track of radius r Two particles A and B start simultaneously from a common point of track Particle A moves with a uniform speed Vo on the straight track whereas particle B moves on the circular track always collinear with centre of track and the point A If the speed of B when it is equidistant from the centre and particle A iso then find the value of k D B

C Tangentially outward D With an acceleration mu 1 6 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 D 4 1 A C 13 A m re CO ne A