Rotation Questions and Answers

U A long solenoid carrying a current I is placed with its axis vertical as shown in the figure A particle of mass m and charge q is released from the top of the solenoid Its acceleration is g being acceleration due to gravity a greater than g m qa 10000000 b less than g

6 Consider a disc rotating in the horizontal plane with a constant angular speed about its centre O The disc has a shaded region on one side of the diameter and an unshaded region on the other side as shown in the figure When the disc is in the orientation as shown two pebbles P and Q are simultaneously projected at an angle towards R The velocity of projection is in the y z plane and is same for both pebbles with respect to the disc Assume that i they land back on the disc before the disc has completed rotation ii their range is less than hal 8 the disc radius and iii remains constant throughout Then R e of P A P lands in the shaded region and Q in the unshaded region B P lands in the unshaded region and Q in the shaded region C Both P and Q land in the unshaded region D Both P and Q land in the shaded region

FH Of A uniform rod of length is pivoted at one of its ends or a vertical shaft of negligible radius When the shaft rotates at angular speed to the rod makes an angle 0 with it see figure To find e equate the rate of change of angula momentum direction going into the paper ml 12 o sin 0 cos about the centre of mass CM to the torque provided by the horizontal and vertical forces F and F about the CM The value of 0 is then such that 1 cos 0 2g 31w 3 cos 0 10 2 cos 0 8 21w 4 cos 3g 1

A hollow hemi sphere of mass m and radius r is released from rest in the position shown Knowing that the hemi sphere rolls without sliding Determine the reaction at the horizontal surface at the instant when it has rolled through 90 Question Type Single Correct Type 1 2 7mg 4 5mg 2

Moment of inertia of a rigid body is expressed in units of kg m There are two rods A and B made of same metal Both of them have equal cross sectional are rod A is double in length as compared to rod B What is the ratio of moment of inertia of rod A to that of rod B

4 Linear and rotational 29 A horizontal disc is rotating about a vertical axis passing through its centre If an insect moves from centre to rim then the angular momentum of the system 1 Decreases 2 Increases 3 First decrease and then increase 4 Remains constant gh Work

5 8 A particle of mass m is projected at t 0 from a point P on the ground with speed v at an angle of 45 to the horizontal Find the magnitude and direction of the angular momentum of the particle at time tr v g Ans 3 nvo 2 2g

0 A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg She produces an angular acceleration of 30 00 rad s and her lower leg has a moment of inertia of 0 750 kg m What is the force exerted by the muscle if its effective perpendicular lever arm is 1 90 cm

4 0 20 Nm An automobile moves on a road with a speed of 54 km h The radius of its wheels is 0 45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m2 If the vehicle is brought to rest in 15s the magnitude of average torque transmitted by its brakes to the wheel is 1 10 86 kg m s 2 3 6 66 kg m s 2 wo metal wire 2 2 86 kg m s 2 4 8 58 kg m s

22 A disc is in the condition of pure rolling on the horizontal surface The velocity of centre of mass is Vo If radius of disc is R then the speed of point P is OP OP R 3 1 W 3 7 v P 2 C 30 V 5 v 3

A rod of mass m and length 21 is connected to two massless strings as shown in figure A wooden disc of the same mass m is fixed at the mid point of th rod in such a way that the plane of the disc is perpendicular to the rod A massless wire is wrapped around the disc and it is carrying a current I There vertically upward magnetic field B at the location of disk Sense of current in the loop when seen from string P side is clockwise P The tension in the string P is A B R mg ITR B 21 Correct Answer mg ITR B 21 X

small spherical metal ball of radius r is lying at the bottom of a stationary container containing liquid of density p as shown in the figure P mospheric pressure Force exerted by liquid on the upper hemispherical part of the sphere is 1 2 3 4 r 3 2 r 3 3Po 7rpg 3Po 4rpg Po 7rpg 2Po 7rpg 2 r 3 4r A

A uniform ladder of length 5m is placed against the wall in vertical plane as shown in the figure If of friction is the same for both the wall and the floor then minimum value of for it not to coefficient slip is A 1 2 B 1 4 5m 4m 3m C 1 3 D 1 5

ected with 2gR from the lowermost point of smooth vertical circular track of radius R as shown Then C B A 1 Particle complete circular path 2 Particle will leave the track between points and C 3 Particle starts oscillation about point A 4 Depends on mass of the particle

47 A rigid body contain only two particle as shown The condition which must be satisfied fagur 1 2 1 V 30 2 3V V 0 2 60 B 3 2V V 0 4 V 3V 0

A solid cylinder attached to horizontal massless spring can roll without slipping along horizontal surface Find time period of oscillation 1 M R G Question Type Single Correct Type 2 2 1 M 2k K wwwwww 3M TV 2k

Two buckets each of mass 27 4 kg spin around a horizontal circle of radius 4 20 m on frictionless bearings with an initial angular velocity of 34 3 rad s Suddenly a mass of 15 5 kg drops straight down into one of the buckets What is the final angular velocity of the buckets Give your answer in rad s to 3 sig digits but do not include units with your answer

A solid sphere is rolling on a frictionles surface shown in figure with a translational velocity v m s If sphere climbs up to height h then value of v should be 10 1 gh 2 2gh 3 2gh

When an external force is applied at the centre of mass of a rigid body at rest then it undergoes 1 Only translatory motion 2 Only rotatory motion 3 Both translatory and rotatory motion 4 An oscillatory motion

Q20 A solid sphere has the same mass and radius as a thin spherical shell The ratio between their moment of inertia about a diameter is O A B a 1 2 b 1 c 3 5 d 5 3 O C O D O Other 1 pc

A flywheel of mass 50 kg and radius of gyration about its axis of rotation of 0 5 m is acted upon by a constant torque of 12 5 N m Its angular velocity at t 5 s is 2 rad s 5 rad s O 10 rad s 12 rad s

Q18 The radius of gyration of a 1 point disc of mass 100 gm and radius 5 cm about an axis passing through its centre of gravity and perpendicular to the plane is a 0 5 cm b 2 5 cm c 3 54 cm d 6 54 cm O A B O C O D

Q19 A thin uniform circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to the plane with angular velocity D Another disc of same mass but half the radius is gently placed over it coaxially The angular speed of the composite disc will be a 5 4w b 4 5w c 2 5w d 5 2w O A O B O C O D O Other 1 po

A uniform round object of mass M and radius R is placed on a rough plank of mass M which is placed on smooth surface Round object is given velocity vo towards right and it starts perfect rolling on plank after some time Description of round body is given in Column l Velocity of round object and plank when perfect rolling begins is mentioned in Column II Match the entries in Column l with entries in column II Mvu R h gggy MMGR JEG ch fac aag 92 2d 55 M 3 ch ych gest a za 21 Macr azgat effe vo an u a fu uld am uz ho a44 th dis aed 42 YG M grey Gr 21 dagk azg a QCI G H L 4 T I J CH A HIRIN 7 air naich a d am ac ch n fa 1 1 ufafu Ama s 11 A a Column l Solid sphere Hollow sphere CATA Ring C CRY Vo Disc d ucha a p t Column II 7 9 N Vo vo VO P qr S

elar Anstyals through Continuous Exercise The figure shows three identical rods each of mass M and length L then the moment of inertia of the system about axis AB will be 1 A ML 12 2 ML B ML 3 3 4 9 ML2 2 1 M 3 If C

A force is applied on a rod of mass M and lenght L at a distance of L 4 from the hinge point then calculate the force is exerted by the hinge on the rod in order to keep the rod in equilibrium L 4 1 Mg upwards 2 Mg downwards 3 2 5 Mg upwards 4 1 5 Mg downwards

Two coplanar uniform identical rings of equal mass m and radius R are rigidly attached to each other at the periphery as shown One ring wears a bead of mass m The bead can slide freely without friction The other ring is hinged at point P in such a way that the structure of two rings can freely rotates about horizontal axis passing through point P The rings and beas are released from rest from position shown Then just after release O Bead The magnitude of angular acceleration of ring is 5g 17R 20 The magnitude of angular acceleration of the structure of rings is 972 20 The magnitude of acceleration of bead is 7 The magnitude of acceleration of bead is 85g g p

The moment of inertia of a uniform thin rod about its perpendicular bisector is I If the temperature of the rod is increased by At the moment of inertia about perpendicular bisector increases by coefficient of linear expansion of material of the rod is a a Zero b la st c 2 la At d 3la At

17 Two uniform rods of mass m and length I form a cross moment of inertia of cross about an axis parallel to CD passing through A is ml 3 Sol Answer 2 1 2 7m 12 A 10 D B 12 D

A bullet of mass m is fired horizontally into a large sphere of mass M and radius R resting on a smooth horizontal table m M A The bullet hits the sphere at a height h from the table and sticks to its surface If the sphere starts rolling without slipping immediately on impact then 2013 h 4m 3M R 2 m M C 6 h R 10m 7M 5 m M B D h R T 2R m M m 2M h 4m 3M m M R

If the 16 kg ball has a velocity of 3 m s when it is at the position A along the vertical path determine the tension in the cord and the increase in the speed of the ball at this position Figure 1 igure 2m 8 45 3m s 1 of 1 Part Dete Expr T Su Part Dete Expr a

14 A hollow cylinder and a solid cylinder having different mass diameter are released from rest simultaneously from the of an inclined plane Which will reach the bottom first a solid cylinder b cant be determined without knowing their masses c hollow cylinder d cant be determined without knowing their diameters

5 Two identical uniform rod each of mass m and length joined perpendicular to each other An axis passes through junction and in the plane of rods Then M I of system about the axis is m m I K 90 m I my

A uniform rod of mass 12 kg and length 4 m is hung from two string of equal length from a ceiling as shown in fig Determine the tension T in N in the string take g 10 m s T 30 4 0 4

A disc of mass M radius R moves under gravity while unwinding string under non slip condition Mark the correct statement s AY M X Acceleration of the centre of the disc is in direction 0 Rate of change of angular momentum L of disc d about a point along string is in k direction dt Angular momentum of disc is conserved about centre of mass Rate of change of angular momentum dL of disc about center of mass is in direction dt

A wire of mass M and length L is placed along x axis with end A at origin The linear mass density of the rod varies as X where x is distance from end A is a constant A A B C B X The value of is 2M Moment of Inertia of the rod about an axis passing through A and parallel to y axis is ML Moment of inertia of the rod about an axis passing through ML COM of the rod and parallel to y axis is 18 Moment of inertia of the rod about an axis passing through B

ottom oI A wheel of radius R and mass M is placed a fixed step of height R as shown in the figure A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping Consider the torque t about an axis normal to the plane of the paper passing through the point Q Which of the following options is are correct JEE Adv 2017 a b c d P S R If the force is applied at point P tangentially then decreases continuously as the wheel climbs If the force is applied normal to the circumference at point X then t is constant If the force is applied normal to the circumference at point P then t is zero If the force is applied tangentially at point S then t 0 but the wheel never climbs the step

estions 9 and 10 Two coaxial pipes of radius 1m and 1 2 m are have a common horizontal axis A uniform solid spherical ball of radius 0 1m is fitted inside them as shown The inner surfaces are sufficiently rough so that there is no slipping any where On slight displacement the ball starts moving along the gap shown in the downward direction There are 2 possible cases A 1 The inner pipe is held fixed but outer pipe is free to rotate 2 The outer pipe is held fixed but inner pipe is free to rotate All the 3 bodies both pipes ball have same mass of 1kg When ball reaches the bottom the pipe which is free to rotate is rotating with angular 00 velocity Let it be o in 1st case w in 2nd case 00 5 6 B A 1 1 2m 5 6 B 1 1m 000 If the angular velocity of ball at the bottom in the 2 cases is 2 C 27 125 D 3 2 a respectively D 27 o

32 A 30 V 90 W lamp is to be operated on a 120 V DC lines For proper glow how resistance in 2 should be connected in series with the lamp 1 40 3 20 V 30 2 10 4 30 301

A uniform rod of mass m and length is hinged at one end which is released from the position shown in the diagram from rest Rod is free to move in vertical plane when rod becomes horizontal then 0 0 Acceleration of COM of rod is 3g sin 0 2 Acceleration of COM of rod is Force applied by hinge on rod is 3mg sin 6 mg 2 3919 3g cos 0 2 9 Force applied by hinge on rod is 3mg cos 0 3mg 2 4 YA X

one end which is released from the position shown in the diagram from rest Rod is free to move in vertical plane when rod becomes horizontal then y 0 Acceleration of COM of rod is Force applied by hinge 3mg sin 0 mg mi 2 Acceleration of COM of rod is 3g sin 3g 2 on rod is 3g cos 0 2 1 1 1 Force applied by hinge on rod is 3mg cos 3mg

Axniform solid cylinder of mass m and radi2R rests on a horizontal table A string attached to it passes over a pulley disc of mass m and radius R that is mounted on a fricitonaless axle through its centre A block of mass m is suspended from the free end of the spring The string does not slip over the pulley surface and the cylinder rolls without slipping on the table Om

hy not possible to use equation of v like 2gh 1 k2 r2 2 4 AN OSCillatory motion 15 9 A solid cylinder begins to rolls down on 30 incline of length 9 m without slipping The speed of centre of mass at the bottom of plane is 1 3g 2 g 3 2 g 2 4 6g B The pres where F drawn o of initial tank will 11P 11

A uniform rod of mass M and length L is suspended by two smooth hinges 1 and 2 as shown in the figure A force F is applied downward at a distance from the hinge 2 Due to the application of force F the hinge 2 breaks At this instant applied force F is also removed The rod starts to rotate downward about hinge 1 g 10 m s2 Choose the correct statement s F The reaction at hinge 1 before hinge 2 breaks is M L The reaction at hinge 2 before hinge 2 breaks is 2F 3 O The reaction at hinge 1 just after breaking of hinge 2 is zero The reaction at hinge 1 just after breaking of hinge 2 is

A solid cylinder begins to rolls down on 30 incline of length 9 m without slipping The speed of centre of mass at the bottom of plane is 1 3g 2 g 3 2 g 4 6g X The pres where F drawn o of initial tank will 110

A thin uniform rod of mass m and length is hanging freely at rest from its topmost point and is free to rotate about its upper end When it is at rest it receives an impulse J at its lowest point normal to its length Immediately after O The angular momentum of the rod is J 3J 0 Angular velocity of the rod is me 0 The kinetic energy of the rod is 3J 2m 3J 0 The linear velocity of the midpoint of the rod is 2m

A rod of mass M and length L is suspended by a frictionless hinge at the point O as shown in figure A bullet of mass m moving with velocity v in a horizontal direction strikes the end of the rod and gets embedded in it The angular velocity of the rod just after the collision is O mv m M

A particle of mass m attached to one end of a thin light inextensible string moves with speed v in a circle of radius ro in free space Calculate the work required to reduce the radius from ro to r by pulling the other end of the string through a smooth tube that is perpendicular to the plane of the circle Express the result in terms of m Vo To and r

The rigid frame shown in the arrangement consists of 6 identical wires of length L and has linear mass density It is kept on a smooth horizontal table on X Z plane In this region of space an external magnetic field B Bo is applied fed the atas L and 6 4464 art Affaut such Zu GWHA UA A 13 X Z da Ich fach ARRAGA ch Boi fu fa ZE A B D Y Question If there is sufficient friction to prevent slipping and the frame is able to rotate about z axis then the angular velocity with which frame strikes the plane just before the first collision with plane is ufa fhuma ch zicha fay adui qufla 7 am cu 2 31 under gufa cz 44 f 3 d h4 cl ag ch uflu an 841 sm Bud ho da Ugafi cache Ac ugd da Scheldi IB V XL 6IB 5XL 12IB 5XL 5IB B 101 T X

TUS A pulley of radius 2m is rotated about its axis by a force F 20t 5t newton where t is measured in second applied tangentially If the moment of inertia of the pulley about its axis of rotation is 10kg m The number of rotations made by the pulley before its direction of motion reversed is More than 3 but less than 6 2 More than 9 3 More than 6 but less than 9 4 less than 3