Rotation Questions and Answers

37 A floor mat of mass M made up of extensible material is rolled along its length so as to form a cylinder of radius R and kept on a rough horizontal surface If the mat is now unrolled without sliding R to a radius the decrease in potential energy is 2 a MgR c MgR 8 5 b MgR d MgR

RD15 A rod of mass m length is hinged at it s upper end It can rotate in vertical plane It is given angular velocity w so that it can complete vertical circle Find a w b Tension at centre of rod at initial moment

A cord is wound round the circumference of wheel of radius r The axis of the wheel is horizotal and moment of inertia about it is I A weight mg is attached to the end of the cord and falls from rest After falling through a distance h the angular velocity of the wheel will be 1 2 2gh I mr 2mgh 1 mp 3 2mgh 1 2m 4 2gh

Angular momentum and its conservation RD16 A uniform ring is rotating about vertical axis with angular velocity o initially A point insect S having the same mass as that of the ring starts walking from the lowest point P and finally reaches the point P as shown in figure What is the final angular velocity of the ring axis of rotation S 90 P 2

Q10 A force F is acting at a on a body distance d from an axis as shown The torque of this force about the given axis is P a O Fd clockwise b O Fd anticlockwise d O zero axis CO Fd into the plane away from us

0 The magnitude of torque experienced by a square coil of side 12 cm which consists of 25 turns and carries a current 10 A suspended vertically and the normal to the plane of coil makes an angle of 30 with the direction of a uniform horizontal magnetic field of magnitude 0 9 T is a 1 6 N m b 1 2 Nm d 1 8 Nm c 1 4 Nm 8

A mass is whirled in a circular path with constant angular velocity and its angular momentum is L If the radius of the string is now halved keeping the angular velocity and mass same its angular momentum becomes 1 1 1 2 4 3 L 2 2 4 2L

A 3 00kg block is suspended by a string wrapped around a solid disk of radius 10 0cm The mass of the reel is 540 grams a If the block is initially 2 00m above the floor find the speed of the block upon reaching the floor in m s b Find the angular speed of the reel when the block reaches the floor in rad s c Find the tension in the string in newtons d Find the torque exerted on the disk in N m

From a circular disc of radius R and mass 9M a small disc of R mass M and radius is removed concentrically The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is Question Type Single Correct Type 1 2 3 MR 4 MR 19 MR

A uniform cylinder of mass m and radius R is connected with a spring of stiffness k If the cylinder does not slide on the inclined plane the elongation of the spring is amgRsino R r k k vvvvvv J then the value of a is LR

If angular acceleration of the uniform disc just after release from rest position shown 87g NR in figure is then calculate N C is 2 centre of semi circular disc 7 10 m R Semi circular disc C T Smooth

A circular disc of mass 5 kg and radius 1 m rotating with speed 60 rpm about a axis passing through a point on its circumference and lies in the plane of the disc The kinetic energy of the disc will be nearly 250 J 125 J 110 J 220 J

A bobbin of mass M 3 kg consists of a central cylinder of radius r 5 cm and two end plates of radius R 6 cm It is placed on a slotted incline on which it will roll but not slip and a mass m 4 5 kg is suspended from a cord wound around the bobbin as shown in Figure It is observed that the system is in static equilibrium What is the angle of tilt 8 of the incline A B C 0 30 0 45 0 60 0 75 M

A house lizard curls its tail in the mid air to land correctly on a vertical wall while jumping from the horizontal floor Physicists have analyzed the Physics involved in such activities made by the lizards What could be the reason behind mid air tail movements by lizard for the correct landing a Maintaining zero net force about the center of mass b Conservation of angular momentum c Conservation of energy and linear momentum d Having non zero net torque about the center of mass

A thin uniform stick of mass M and length is positioned vertically with its tip on a frictionless table It is released and allowed to fall Determine the speed of its CM just before it hits the table see figure If your answer is Xgl VY then fill value of X Y where X and Y are smallest positive integer fr

A solid cylinder of mass 2 kg and radius 50 cm rolls up an inclined plane of angle o inclination 30 The centre of mass of the cylinde has speed of 4 m s The distance travelled by the cylinder on the inclined surface will be take g 10 m s NEET 2019 Odisha 1 2 4 m 2 2 2 m S

The moment of inertia of a ring about an axis passing through the centre and perpendicular to it plane is I It is rotating with angular velocity o Another identical ring is gently placed on i so that their centres coincide If both the rings are rotating about the same axis then loss in kinetic energy is A 10 2 B Ico 10 C D Ico

A student Amir of mass m is standing on the edge of an horizontal disk of radius R The disc is free to rotate about a frictionless vertical axis passing through its centre Initially the student and disc are at rest At t 0 the student starts to run at his maximum velocity v relative to disc He runs along the circumference of the disc towards his friend Salman in anticlockwise sense Salman is stationary on ground Moment of inertia of disc is I A Time taken to reach Salman is TR V I mR TR B If disc were considered massless time taken to reach Salman is C If disc were considered massless Amir can never reach Salman D Time taken will be minimum if Amir instead of running along circumference runs along diameter towards Salman V

Figld massless rod has three particles with equal masses attached to it as shown in figure The rod is free to rotate in a vertical plane about a frictionless axle perpendicular to the rod through the point P and is released from rest in the horizontal position at t 0 Assume m 1 kg and d 1 m 2d 3 Column II III IV 11 12 13 The angular acceleration of the system in rad s The kinetic energy of the system in joules The angular momentum of the system in kgm s The speed reached by the particle labelled 2 in m s Column i 10 ii Kinetic energy of the system A II ii R C II iii S iv Angular acceleration of the system A 1 ii Q C 1 iv Q Angular momentum of the system A III iv P C D R 2 30 7 2 5 21 35 3 Column III P Maximum Q At t 0 R Minimum S Zero B 1 1 Q D 1 iii Q B II 1 P D II iv P B III i R D III iii P

A uniform circular disc rotating at a fixed angular velocity w about an axis normal to its plane and passing through its center has kinetic energy E If the same disc rotates with an angular velocity 2w about a parallel axis passing through the edge and axis is in the plane of disc its kinetic energy will be O2E 5 E 10 E 12 E

A rod is standing vertically on a smooth surface if the rod is slightly disturbed and it falls towards the right then 1 The center of mass moves vertically downward 2 The center of mass moves towards the right 3 The center of mass moves towards left 4 The center of mass does not move

C 36 Initially a slender prismatic bar AB of weight W and length is falling in a vertical plane with velocity ve and without rotation Fig The end B of the bar slides freely along a smooth vertical wall and the bar makes an angle a with the wall Suddenly the end A of the bar comes into contact with a smooth horizontal floor and there is an impact Assuming no tendency to rebound and that the ends A and B of the bar are frictionless find the angular velocity w with which the bar begins its new motion after impact de wane od toglav lugn trov od to no B d Ag aslige sapuc C Fig 1 236 id free to ro

4 The diagram shows a wheel rolling without slipping along a horizontal road from left to rig A piece of mud on the rim becomes detached at M when the contact between wheel and road is at P Wh f the arrows A B C D E best shows the initial direction of the path followed by the detached partic D Arrow D E Arrow E A Arrow A B Arrow B C Arrow C B A M E

A cylinder of mass M is suspended by two strings wrapped around it as shown The acceleration a and the tension T when the cylinder falls and the string unwinds itself is 1 a g T 2 a 3 a 4 a 9 2 a g 3 2g 39 T T T Mg 2 Mg 2 Mg 3 Mg 6 T Mg

A uniform disc of mass m is attached to a spring of spring constant k and friction is sufficient to prevent slipping of disc Time period of small oscillations 2 1 2 LEIX 2 2 000000007 K 2m 3k R R 2 xam 3 3m 2k 4 2m 3k

A disc of mass M and radius R is rotating about an axis which is lies in the plane of the disc and touching its circumference A hollow cylinder of mass M and radius R rotating about its geometrical axis with angular velocity half of that of sphere The ratio of kinetic energy of Edisc Ecylinder A B 5 1 3 1 C 7 5 is

69 A wheel comprises a ring of radius R and mass M and three spokes of mass m each The moment of inertia of the wheel about its axis is a M m R2 2 M 3m R RO M d oil at pail ondt griezisq odi to got sdi tis te bus baib b M m R M m 2 R

molecule consists of two atoms each of mass m and separated by a distance d At room emperature the average rotational kinetic energy is E then its angular frequency is m Ed B d m C 2 E D Ed

The two identical masses m 2 kg are connected by a light rod of length 1 m placed on a smooth surface Another 4 kg mass 1 moving with speed 3 m s hits B If e choose the correct option 2 2m A B C B m 1m A Velocity of A just after collision is zero Loss of energy after collision between B and C is 4 5 J Impulsive tension of rod during th time of collision is zero Angular velocity of rod just after

A child is standing with his two arms outstretched at the centre of a turntable that is rotating about its central axis with an angular speed wo Now the child folds his hands back so that the total moment of inertia becomes 1 3 times the initial value The new angular speed is Question Type Single Correct Type 1 3w0 5 wo

A uniform rod of mass m length I is hinged at A It is released from the given position so that it rotates about A in vertical plane Which of the following represents the hinge force when rod becomes horizontal Rod is rotating clockwise B

A disc of mass M radius R lies with its centre at a distance a from origin on the x axis Which of the following is correct 1 Moment of inertia of the disc about x axis is MR 4 2 Moment of inertia of the disc about y axis is MR 4 Ma 3 Moment of inertia of the disc about z axis is MR 2 Ma 4 All of these

A standing wave with a frequency of 1100Hz in a column of methane at 27 0 C produces consecutive nodes that are 0 200 m apart What is the approximate value of y for methane The molar mass of methane is 16 0 g mol Take R 25 J mol K 3 O 7 5 O 4 3 O 615 4

The total torque about pivot A provided by the forces shown in the figure for L 3 0 m is 70 N 90 N 80 N 60 A 1 210 Nm 2 140 Nm 60 3 95 Nm 90 KI Question Type Single Correct Type 30 60 N 50 N B

of mass m moving with velocity vo hits a stationary thin uniform ring of equal mass m lying horizontally on a smooth horizontal surface tangentially and sticks to it The angular speed of system after collision is m Vo 1 2R Vo m R

A block of mass M 5 50 kg is connected by a string to a frictionless pulley or radius r 0 330 m and moment of inertial The block accelerates down along the incline at a 2 35 m s2 as the pulley rotates clockwise The incline makes an angle 37 00 with the horizontal and is completely frictionless M Using Newton s Laws for linear and rotational motion determine the moment of inertia of the pulley You may need to determine the tension force that produces the torque on the pulley

When a 12000 joule of work is done on a flywheel its frequency of rotation increases fro 0Hz to 20Hz The moment of inertia of flywheel about its axis of rotation is n 10 A 1 688 kgm B 2kgm C 1 5 kgm D 1 kgm

A disc of mass m and radius R is given a translation velocity v and angular velocity 0 V R the rough inclined plane with angle of inclination 8 as shown in figure The time after which v Ro relation holds good again is Nvo gsing Find the value of N v R c0 Vo on 1 6 tan0

A disc of moment of inertia I is rotating in horizontal plane about an axis passing through a centre and perpendicular to its plane with constant angular speed o Another disc of moment of inertia 1 having zero angular speed is placed coaxially on a rotating disc Now both the discs are rotating with constant angular speed The energy lost by the initial rotating disc is 2 1 1 1 1 2 00 B 11207 2 1 1 11 22 2 11 2 007 D 2 1 1 I I 00

A disk has a moment of inertia of 2 50 x 10 2 kg m2 and spins on a frictionless axis through its center at an initial angular speed of 22 2 rad s A ring initially not rotating of mass 0 250 kg and radius 0 200 m is dropped vertically onto the disk and sticks so that the combination rotates about a common axis through their centers What is the new angular speed of the system Note Iring MR

PHYSICS NA 5 10 200 W rad s Take g 9 8 m s A one meter long scale is held vertically with one of its ends on a rough horizontal surface while its other end is allowed to fall Assuming that its ends on the floor does not slip the angular the scale when hits the horizontal surface Round the answer to two decimal places

A uniform disc of mass m and radius r is attached with 5 point masses of mass m on its rim The total moment of inertia of the system is about am axis passes through the centre and perpendicular to the plane of disc 1 1 1 mr 3 7 2 mr 2 5 mr 6 mr 4 r

008 10 0 points A weight with a mass of 120 kg is suspended from a point at the right hand end of a uni form boom with a mass of 68 kg A horizontal cable at an elevation of 6 m is attached to the wall and to the boom at this same end point The boom is also supported by a pivot at the origin of the coordinate axes on the same wall Vertical Height m 10 T 68 kg 2 1 120 kg 0 0 1 2 3 4 5 6 7 8 9 10 Horizontal Distance m Figure Drawn to scale Calculate the tension T in the cable The acceleration of gravity is 9 8 m s

A small particle of mass m is attached at B to a hoop Ring like of mass m and radius r whole system is placed on the rough horizontal ground The system is released from rest when B is directly above A and rolls without slipping Find the angular acceleration of the system at the instant when AB becomes horizontal as shown in the figure A 3g r 5g 8r 3g 8r B

A square frame ABCD is formed by four identical rods each of mass m and length I Thi Frame is in X Y plane such that side AB coincides with X axis and side AD along Y axis Th moment of inertia of the frame about X axis is 2ml B C 3 5ml 3 A 4ml 3 D m1 12

Water enters vertically and steadily into a sprinkler shown below and is discharged at a rate of 20 L s through ach nozzle Each nozzle has a discharge area of 2 cm Determine the torque required to prevent the sprinkler om rotating Assume p 1000 kg m for water 2 18 sm fo E 15 cm 1

4 Zero 151 neet prep A ring is rolling without slipping on a horizontal plane with velocity v and acceleration a The acceleration of point of contact is O 1 Horizontally towards right 2 Vertically upward 3 Vertically downward 4 Zero High Yielding Test Series Part Test 5 Half XIth Contact Number 9667591930 8527521718 Page A solid cylinder is rolling without slipping on a horizontal surface If VA VB and Vc are instantaneous velocities of points A B and C on the cylinder then which of the following is correct A 60

1 90 5 J 3 60 7 J 2 48 J 4 100 8 J As shown in the figure a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel disc of radius r and mass m When released from rest the bob starts falling vertically When it has covered a distance of h the angular speed of the wheel will be 1 2gh m r 3 XT T Ima m img 1 4gh 3

2 then of the into a of the own in 2 VA VB VC 3 VA VC VB 4 Vc VA VB 159 A uniform cubical block of side L rests on a rough horizontal surface with coefficient of friction A horizontal force F is applied on a block as shown If there is sufficient friction between the block and the ground then the torque due to normal reaction about its centre of mass is F 1 Zero 2 FL FL 3 2 4 3FL 0 2

The axis of rotation of a purely rotating body O Must pass through the centre of mass O May pass through the centre of mass O Must pass through a particle of the body None of these