Rotation Questions and Answers

A thin circular ring of mass M and radius R rotates about an axis through its centre and perpendicular to its plane with a constant angular velocity Four small spheres each of mass m negligible radius are kept gently to the opposite ends of two mutually perpendicular diameters of the ring The new angular velocity of the ring will be M 1 0 4m 2 M 4m M 3 M M 4m 0 M M 4m

body of mass M and radius of gyration K is rotating with angular velocity w 3t t2 rad s The torque acting on it at t 1 s will be O 4MK O 5MK O 2MK O 6MK

A sphere of mass 2kg and radius 0 5 m is rolling with an initial speed of 1 ms 1 goes up ar inclined plane which makes an angle of 30 with the horizontal plane without slipping How low will the sphere take to return to the starting point A A 1 0 60 s 30 2 0 52 s

A solid uniform ball of mass m and radius R collides elastically with a rough fixed inclined surface as shown Velocity and angular velocity of ball just before collision are Vo and wo 5Vo Choose correct option s R 37 Rough u

A 20 0 kg steel cylinder has an 80 cm diameter What is the cylinder s moment of inertia when it is rotated through an axis parallel to its length and 10 cm from its center A 1 8 kg m B 6 6 kg m C 1 8 x 10 kg m D 6 6 10 kg m

If I is the moment of inertia of a thin rod about an axis perpendicular to its length and passing through its one end and 2 is moment of inertia of ring about an axis perpendicular to plane and passing through its centre formed by bending the rod then O N w t 2 3x2 1 is

R A disc of radius R and thickness 48 inertia about an axis passing through its centre and perpendicular to its plane Disc is melted and recast into a solid sphere The moment of inertia of the sphere about its diameter is 10 01 10 12 20 has moment of

A body is rotating with angular velocity 20 rad s If its kinetic energy is 400 J then its moment of inertia is O 2 kg m O 0 5 kg m O 4 kg m O 1 kg m

6 m s As shown in the figure a ball Consider it a hollow sphere is thrown in the rough horizontal surface It is moving in such a way that it slides with a speed V Vo initially without rolling on a rough horizontal plane After a while the ball starts performing pure rotation Determine the translational speed of the ball once it starts rolling without sliding M A 18 m s 5 R Vo F 0

A body rolls down an inclined plane If its kinetic energy of translation motion is 50 of its total energy then the body is O Solid cylinder O Solid sphere O Disc O Ring

2 A symmetric Yo Yo of mass M has an axle of radius b and a spool of radius R Its moment of inertia about the centre of mass can be taken to be MR The Yo Yo i placed upright on a table and the string is pulled with a horizontal force F as shown The coefficient of friction between the Yo Yo and the table is u What is the maximum value of F in N for which the Yo Yo will roll without slipping Take 0 1 M 2kg R 1m b m g 10 m s R F

A uniform circular disc of mass 1 5 kg and radius 0 5 m is initially at rest on a horizontal frictionless surface Three forces of equal magnitude F 0 5 N are applied simultaneously along the three sides of an equilateral triangle XYZ with its vertices on the perimeter of the disc see figure One second after applying the forces the angular speed of the disc in rad s is X Z

Two identical ladders each of mass M and length L are resting on the rough horizontal surface as shown in the figure A block of mass m hangs from P If the system is in equilibrium find the magnitude and the direction of frictional force at A and B A E 0

A solid sphere of mass m is released on the plank of mass M which lies on an inclined plane of inclination as shown in figure There is sufficient frictional force between sphere and plank and the minimum value of co efficient of plank and surfaces is u to keep the plank at rest Then frictional force between sphere and plank is mg sin 8 when plank is at rest 7M 2m tan 0 7 M m the value of u is If there is no friction between the plank and inclined plane then acceleration of plank is less than g sin 0 If there is no friction between plank and inclined plane then friction force on the sphere is zero 8 m

and angular speed of the solld sphere when it reaches point A Given friction is sufficient for pure rolling pls explain briefly friction sufficient for rolling 2nd case if it is not sufficient A

A horizontal moving ball has velocity vo just before impact at one end of a vertically hanged rod having same mass Other end of rod is hinged Find possible speed of the ball just after impact w collision is elastic A B C DI 2 2V 3 Vo 3 Nona

V R M R Four spheres are rigidly attached to a crossbar frame of negligible weight A couple moment M is applied as shown by the curved arrow In addition a couple of forces R is applied to the centers of spheres B and D as shown Also a couple of forces Q is applied to the centers of spheres A and C as shown The direction of the forces relative to the crossbar frame always remains as shown

A square loop ABCD of side length a and mass m of each side is kept in a uniform magnetic field region B B as shown in the figure The loop is constrained to rotate only about the y axis It rotates only due to the torque of the magnetic force acting on it Calculate its angular speed in rad s when it has rotated through an angle 90 Initially the loop was lying in the x y plane The loop is carrying current I as shown in 31B figure Given m 4

Q56 NTA Test 44 Numerical One fourth length of a uniform rod is placed on a rough horizontal surface and it starts rotating about the edge as soon as we release it Th starts slipping on the edge when it has turned through an angle If the coefficient of friction between rod and surface is 4 and it satisfies relation z tan 8 4 then what is the value of z Take g 10 m s

The figure shows a uniform rod of length moving such that velocity of its centre of is v If the end A of the rod is suddenly fixed The angular velocity of the rod will be A B 0900 O 3 4 O 09 2020 NIS

A simplified model of a bicycle of mass M has two tyres that each comes into contact with the ground at a point The wheelbase of this bicycle the distance between the points of contact with the ground is w and the center of mass of the bicycle is located midway between the tyres and at height h above the ground Air resistance is ignored W W Case 1 Assume that cycle is accelerating rightwards and the cyclist is pedalling without braking Both tyres roll purely 16 The direction of friction on the tyres is A Froward on both B Backward on both C Forward on front backward on rear D Forward on rear backward on front Case 2 The bicycle is moving to the right but slowing down at a constant rate The acceleration has a magnitude a A ssume that the coefficient of sliding friction between each tyre and the ground is u and that both tyres are skidding sliding without rotating Express your answer in terms of w h M and g 17 What is the maximum value of u so that both tyres remain in contact with the ground h 2h B Center of mass of bicyle W

1 28 A rod of length 1 m is sliding in a corner as showr in the figure below At an instant when the rod makes an angle of 60 with the horizontal plane the downward velocity of point A is 1 m s What is the angular velocity of the rod at this instant a 2 0 rad s c 0 5 rad s A 60 B b 1 5 rad s d 0 75 rad s

if rotational kinetic energy of spinning hoop A is 32 joules what is the rotational kinetic energy of the hoop B The rotational speed radius and mass of each hoops are labelled in the sketches Hoop A 32 joules 16 joules 8 0 joules 4 0 joules None in the list 2r 2m 200 O Hoop B m

A circular disc rotates freely about a vertical axis through its centre with angular velocity A ring having the same mass and radius of the disc is placed on the disc and the system now rotates with an angular velocity 2 about the same vertical axis Then w w is 01 13 01 12 O 03 10 O O W N

A ring of mass m 1 kg and radius R 1 25m is kept on a rough horizontal ground A small body of same mass m 1kg is struck to the top of the ring When it was given a slight push forward the ring started rolling purely on the ground What is the maximum speed of the centre of the ring in m s A 1 B 5 C 2 D 10

What is the torque in Nm on the cylinder when mass m is accelerating down with 2 0 m s 2 Assume radius of the cylinder r 0 32 m rotational inertia of the cylinder is 2 0 kg m 2 m 6 0 kg and use g 9 8 m s 2 if needed m 10 axis

000 O A uniform disc of mass m and radius R is gently kept on a horizontal rough surface coefficient of friction u with an initial angular velocity wo keeping its plane vertical Find a the final velocity of its centre and the angular velocity after sufficiently long time b the dissipation of total mechanical energy for a long time because of friction 1 A sc from a a the mo sha of pla cono a

A horizontal platform is rotating with uniform angular velocity around the vertical axis passing through its centre At some instant of time a viscous fluid of mass m is dropped at the centre and is allowed to spread out and finally fall on ground The angular velocity during this period const 1 decreases continuosly 2 decreases initially and increases again 3 remains unaltered COAM I 4 Increases continoushu IT WI

A 2cm The figure shows a uniform slab of mass 7 kg What is its moment of inertia in kg cm about the axis normal to the plane of drawing and passing through the point O It is given that the sides OA and OC are equal i e OA OC 90 790 B 3 10 cm 3 00 0 00

A spring mass system mass m spring constant k and natural length rests in equilibrium on a horizontal disc The free end of the spring is fixed at the centre of the disc If the disc together with spring mass system rotates about it s axis with an angular velocity o k mo the relative change in the length of the spring is best given by the option 1 3 2 2 mo 3 k mo 2 4 2mo k 2 mo

A uniform rod of length 7 is pivoted at point A it is struck by a horizontal force which delivers an impulse J at a distance x from point A as shown in figure impulse delivered by pivot is zero if x is equal to A B X C 21 D 31

Q10 90 Moment of inertia MI of four bodies having same mass die respectively 4 M of a ring of radius R about tangent axis in the plane of ring 1 M of a disk of radius R about an axis perpendicular to disc and passing through centre 13 M of a thin hollow sphere of radius R about diameter axis L M of a rod of length 2R about an axis through the end and making an angle 30 with rod 11 13 1 9 4 3 2 01111 9 3 4 2 4 12 13 14 9 3 4 1 412 13 13 4 309 2

Two rigid bodies A and B rotate with angular momenta L and Lg respectively The moments of inertia of A and B about the axes of rotation are IA and I respectively If I IB 4 LA 5LB rotational kinetic energy K of A and the rotational kinetic energy KB of B then A A 25 K 4 KB 1 KB 3 KR 1 4 2 54 K A 100 4 KR

3 Centrifugal force 4 Frictional force A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity w The force exerted by the liquid at the other end is 1 3 MLO 2 MLO 4 2 ML ML 2 1 3

A ring rolls without slipping on a horizontal surface At any instant its position is as shown in the figure Choose the CORRECT statement s A B 0 10 Section ABC has greater kinetic energy than section ADC Section BC has greater kinetic energy than section CD DSection BC has the same kinetic energy as section DA The sections AB BC CD and DA have the same kinetic energy

The diagram shows a semicircular ring carrying uniformly distributed charge 2 C on it The radius of the ring is 4cm A point charge 2 C is taken slowly from the point 0 0 8cm to 0 8cm 0 The magnitude work done is equal to 4J After fixing the charge at its new position the ring is rotated in anticlockwise sense about the x axis as seen from 16cm 0 0 by an angle 1 2 What is the magnitude of work done in electric field during the rotation of the ring Initial position of Point Charge X

It is well known that the radius of earth at equator is more than radius at poles To estimate this let s assume two tunnels in earth 1 along the axis of rotation of earth and 2 along equatorial radius Both are filled with liquid Assuming earth s angular velocity as radius at equator is density of fluid as p find the difference in length of liquids in both tunnels in steady state Assume R g FR4 2 R4 R4 4 R4

7 A wheel with rotational inertia 0 04 kg m and radius 0 02 m is turning at the rate of 10 revolutions per second when a frictional torque is applied to stop it How much work is done by the torque in stopping the wheel A 0 0008 J B 0 47J C 2 J D 27 J E 87 J

Figure 5 show forces applied to a wheel that weighs 20 N The symbol W stands for the weight In which diagram s is are the wheel in static equilibrium 20 N W A A C B A C B D C and A E D 10 N 10 N 10 N 20 N W B 10 N 10 N C 10 N 10 N W D 10 N

sphere rolling on a Wedge A uniform solid sphere of mass m and dius r rolling without slipping down on an inclined wedge of same mass s shown Find velocity of wedge when sphere reaches the bottom of

he same art from ground which wheel 1 3 t T 20 Select incorrect statement 2 t T 4 t 2T 1 During rolling the force of friction acts in the same direction of motion of the centre of mass of the body 2 For perfectly rolling motion work done against friction is zero 3 The instantaneous acceleration of the point of contact during rolling is non zero 4 Both 2 3

6 A solid sphere and a solid cylinder of same mass are rolled down on two inclined planes of heights h and h respectively If at the bottom of the plane the tw objects have same linear velocities then the ratio of hy h is a 2 3 c 14 15 lo n Ispitngl Tod mi b 7 5 10 d 15 14 te od llw

57 Consider three solid spheres sphere i has radius mass 3m and mass m sphere ii has radius r and sphere iii has radius 3r and mass m All can be where they will roll without slipping to the bottom placed at the same point on the same inclined plane If allowed to roll down the incline then at the bottom of the incline a sphere i will have the largest speed b sphere ii will have the largest speed c sphere iii will have the largest kinetic energy d all the spheres will have equal speeds ole m of pla

View in English solid sphere of mass m rolls without slipping down on inclined plane with an acceleration a The frictional force on the solid sphere due to surface of the plane is 2ma 3

a moment From 30 to 20 kg m s in a period of second The average torque acting on flywheel during this period is uestion Type Single Correct Type 10 Nm 2 2 5 Nm 3 5 Nm 4 1 5 Nm

Question No 31 A solid cylinder of mass M and radius R rotates about an axis passing through its centre making 60 rpm Its kinetic energy of rotation is O 4 MR 2 2 MR MR 6 MR

Question No 42 A disc of mass m and radius R is rolling without slipping as shown in the figure The velocity of the point P will be O 3RD 2 RIN 80

Question No 41 A uniform sphere of mass m and radius r rolls without slipping down an inclined plane inclined at an angle 53 to the horizontal What is minimum value of coefficient friction at which slipping is absent C IN

The linear speed of a uniform spherical sh after rolling down an inclined plane vertical height h from rest is Question Type Single Correct Type 1 2 x 1 3 10gh 7 4gh V 5 6gh V 5

Question No 43 A hoop of radius r weighs m kg It rolls along a horizontal surface so that centre of mass has speed v m s How much work has to be done to stop it O my C 5 My