Rotation Questions and Answers

uestion No 20 ollow hemisphere is fixed and has radius R 8 r where r is radius of small solid sphere released at top as shown Sphere rolls without slipping Then sphere reaches bottom velocity of top most point of sphere is

Q 88 A light rod of length is pivoted at distance f 4 from the left end has two masses mo and m attached to its ends such that rod is in equilibrium Find m terms of mo mo A B C Torque about P is zero D Torque about P is not zero mo 8 4 m

A solid cylinder starts rolling down an inclined plane without slipping The speed of axis of cylinder when it has moved down by vertical displacement his 4gh 2gn Read More agn

d If for a real differential wheel and axle system the efficiency of machine is 80 calculate the effort required to lift a load of 500 N Also calculate the number of revolutions that the machine 15 cm would make in lifting the load through a distance of 25 cm Given diameter of wheel diameter of axles 10 cm and 5 cm

A uniform triangular plate of mass 12 kg and 2 m is rotated about the axis shown with constant angular speed of w 3 rad s The kinetic energy of plate in joule is 00 Answer

Q 81 Figure shows a horizontal rod AB which is free to rotate about two smooth bearing system Two identical uniform rods each of mass m are attached to rod AB symmetrically about the centre of mass O of the rod AB All the dimensions are given in the figure The system is rotating with constant angular velocity in such a way that the upper rod is coming outward from the plane of the paper in the position shown Gravity can be assumed to be absent in the experiment Then choose the correct option s A The hinge reaction at A on the rod AB is downward B The hinge reaction at B on the rod AB is upward C The hinge reaction at B on the rod AB is downward D The angular momentum of the system about point O is not along the rod AB

A uniform rod of mass M and length L is held vertically on a smooth horizontal surface when the rod is released choose the correct alternative s DE The centre of mass of the rod accelerates in the vertical direction Initially the magnitude of the normal reaction is Mg When the rod becomes just horizontal the magnitude of the normal reaction becomes Mg 2 When the rod becomes just horizontal the magnitude of the normal reaction becomes Mg 8

In the figure shown a plank of mass m is lying at rest on a smooth horizontal surface A dise of same mass m and radius ris rotated to an angular speed and then gently placed on the plank If we consider the plank and the disc as a system then frictional force between them is an internal force Momentum of the system changes due to external force only It is found that finally slipping cease and 50 of total kinetic energy of the system is lost Assume that plank is long enough is coefficient of friction between disc and plank 24 Final velocity of the plank is r000 A B Fog m r 000 m O rog D None of these

Q 85 In the adjoining figure the dise of mass M and radius R is in equilibrium The extension in spring 1 is R 100 The extension is spring 2 and the compression in spring 3 are A R 100 B R 150 www 2 2K 0000000 0000000 3 3K C oooooo HO 3R 200 D R 250

Four point masses each of value m are placed at the corners of a square ABCD of side The moment of inertia of this system about an axis passing through A and parallel to BD is b 3m 2008 d m a 2m c 3m2 11 ADAD

A bowling ball has a mass of 5 6 kg and a radius of 26 cm If it is rolling down a lane with a speed of 9 2 m s what is the angular momentum of the ba kg m s

A thin uniform rod of length L and mass mis pivoted at a point at a distance L 3 from one of its ends such that it can rotate freely in the vertical plane The rod is released from rest in the horizontal position as shown Which of these options is are correct L 3 The initial acceleration of the centre of mass of the rod is 3g 4 3mg 4 The force applied by the pivot on the rod just after it is released is O As it rotates the maximum angular velocity the rod attains is At the instant the angular velocity of the rod is maximum the acceleration of its centre of mass is bola g

Question No 18 Starting from rest a cylindrical body of uniform density and mass m is allowed to roll down from the top of a fixed inclined plane of total height h The upper half of the inclined plane is rough and the friction coefficient is high enough to allow pure rolling and the lower half of the inclined plane is frictionless The velocity of the centre the ratio R is of the body upon arriving at the bottom of the plane is 14g If the moment of inertia of the body about its central axis is 19 h 2 h 2

A hollow cylinder is released from the top of an inclined plane of inclination 30 and length 5 m If the cylinder rolls without slipping then its speed when it reaches the bottom is 30 2 5 m s O 5 2 m s 5 m s O 10 m s

Starting from rest a cylindrical body of uniform density and mass m is allowed to roll down from the top of a fixed inclined plane of total height h The upper half of the inclined plane is rough and the friction coefficient is high enough to allow pure rolling and the 14gh lower half of the inclined plane is frictionless The velocity of the centre of the body upon arriving at the bottom of the plane is 9 If the moment of inertia of the body about its central axis is mk the ratio R is

Paragraph A thin uniform rod of mass 2m and length L hinged at its upper end hangs in equilibrium A small bullet of mass mis fired horizontally with velocity v The bullet hits the rod very close to its bottom end and gets embedded in it 2 m L 1 in

A beam is of T section as shown in figure The beam is simply supported over a span of 4 m and carries a uniformly distributed load of 1 7 kN m run over the entire span Determine the maximum tensile and maximum compressive stress 8 100 mm 50 mm 150 mm

A door 1 6 m wide requires a force of 1 N to be applied at the free and to open or close it The force that is required at a point 0 4 m distant from the hinges for opening or closing the door is A 1 2N B 3 6N C 2 4N D 4N

As shown in figure there is a flat plank at rest on a very slippery surface You have disc of radius a and mass equal to the mass of the disc say M You rotated the disc with an initial angular speed and carefully placed it on the plank The coefficient of friction between the disc and plank is You noticed that finally when the slipping stops the 50 of the total kinetic energy of the system is lost If the plank is long enough determine the time when slipping stops after placing the disc

The figure shows a table whose weight in 100 N on which a box of weight 60 N is placed on the center of its upper bench The table has two legs and is assumed to have homogeneous density Assuming static equilibrium you are required to find the force from the ground on each leg using the following two methods 1 Analyze the table and the box as one body Take a free body diagram for the table with the box and analyze the entire system 10 points 2 Analyze the table and the box as two different bodies in contact Take one free body diagram for the box and another for the table 40 points You need to clearly identify all the forces and the action reaction pairs in your solution when using each of the above methods 60 N box 100 N table 1 m

two gear combination shown The in the drawing is being used to lift the Load L with a Constant upward speed of 2 50 m s The rope that is attached to the load c 0 170 m rad s 0 300 m L is being wound onto a cylinder behind the big gear The depth of teeth of gears is negligible compared to the ra Determine the angular velocity magnitude of smaller gear 17 a rad s 250 250 17 b 25 x d 25 x 30 17 m 30 rad s 2 50 rad s

QS without slipping on the horizontal surface as shown List gives the four different shapes of the given solid body and corresponding values of F and h while List Il gives the magnitude of some quantities List l QE 1 For a ring F 2mg h 23 AB Lot PT Il Paper 2 PCM 000000 1 8 QS II III For a hollow sphere F For a disc F mg h IV For a solid sphere F ags SCO A Options A B C D 3 WM 1 agE R2 3R 4 P110707 CID PNBT LEXAM PT 2 5mg R 8 3 mg 2 1 h 1 h I P II R III Q IV S I Q II P III S IV U 3R 5 FIITJEE Ltd FIITJEE House 29 A Kalu Sarai Sarvapriya Vihar New Delhi 110016 Ph 26515949 26569493 Fax 26513942 website www fuitjee com I P II T III R IV S I T II Q III R IV U P Q R S T List II U 1 1 3 7 If acceleration of the ring is ao then the acceleration of the different shapes of the body in ao units will be 8 21 1 4 2 NIN 7

In the figure shown a smooth ring is connected to rod D AB while rod CD passes through ring At the given instant angular velocity of rod AB about hinge A is 1 rad s and AC CB Instantaneous angular velocity of rod CD about hinge C is A 1 rad s B rad s C 3 2 rad s D 3 2 rad s B 1 rad s 30

i If the axis of rotation is non inertial having acceleration a generally Text l does not hold because the pseudo force ma on each particle will produce a pseudo torque In this case Text pseudo l E

On a solid sphere lying on a horizontal surface a force F is applied at a height of R 2 from the centre of mass The acceleration of a point at the top of the sphere is there is no slipping at any point B A 15F 7M 15F 14M C 30F 7M D F M

Two smooth cylinders with diameters 250mm 400mm respectively are kept in a groove with slanting surfaces making angle 60 30 as shown in fig Determine the reactions at contact points A B and C 500 N 800 N Ans R 352 69N R 297 3N Re 1125 83N

5 a A uniform rod of mass 10 kg pinned at O and its ends are welded by sphere of mass 20 kg at upper end and circular disc of mass 15 kg at lower end as shown in Fig 5 a Find moment of inertia about pinned axis 10 cm 20 cm 30 cm 12 cm Fig 5 a b Calculate the moment of inertia of the shaded area Semicircle Triangle shown in figure about the point O Given radius of semicircle 30 mm Fig 5 b

A stone of mass 0 1 kg is projected with a velocity a 20 2 m s from the origin of an xy co ordinate axi system at an angle of 45 with the horizontal Th angular momentum of the stone about the origin after second is take g 10 m s 1 10k kg m s 2 10k kg m s 103

183 A uniform rod AB of mass m and length rest on a smooth horizontal surface An impulse J is applied at a distance from centre C of rod as shown If angular velocity of rod is then Nis NJ me B 13

57 A constant force acting at the centre of a uniform disc of radius r is always perpendicular to the plane of the disc The disc can rotate about a chord at a distance from the centre of the disc For what value of x will the angular acceleration of the disc be maximum a c 3 7 2 b e 3 d 2

A wheel comprises of a ring having mass 2m and two rods mass m and lengt I along two diameters as shown Find moment of inertia of the wheel about a axis passing through point P and perpendicular to the plane of wheel 2 3 m m 5 m 7 mp 2m

A uniform rod of mass m and length L is at rest on smoot surface A small ball of equal mass m moving with veloci Vo hits one end of rod perpendicularly as shown and stick to it The angular speed of rod after collision is m 12V 5L 8V 3L 5V 6L CV

The moment of inertia of a uniform thin rod of mass m and length l about two axes PQ and RS passing through centre C of the rod and in the plane of the paper are IpQ and IRS respectively Then find the value of lpq IRS me A 3 me 6 C B D me 12 2m 3 S P 68 22 R

Q No 3 Marks 4 00 2 00 of any correct option s will result in 2 marks View In English A thin ring is free to rotate in the vertical plane about O Ring is released from rest at 0 0 when ring rotates through angle 0 C 0

By joining three rods of equal mass m and equal length 1 an equilateral triangular structure is formed as shown in figure Corner C of the structure is hinged and free to rotate about horizontal axis in vertical plane corner B of the structure is supported by a light string so that the C m of structure lies on horizontal line After burning support B The maximum speed of A is found as x unit Find the value of x take g 1 3 Cm B

Zero Marks In all other cases The moment of inertia of a uniform circular disc about its diameter is 2kg m If its moment of inertia in kg m about an axis passing through its circumference and perpendicular to its circular face is 61 then value of I is

o 3 If correct numeric answer is typed in the provided space o 0 in all other cases A right triangle of side lengths a b c is formed using there thin rods of same material which are firmly fixed to each other The triangle which is initially placed vertically into a horizontal plane on its edge b tumbles down from this unstable position a 30 cm c 50 cm The velocity of the vertex B when it hits the horizontal plane provided that the triangle does not slides on the ground is B C

A solid sphere and a hollow sphere are released from rest on two identical inclines from same level Coefficient of friction is not same but sufficient to allow pure rolling When they reach bottom which of the following are same Time Kinetic energy Velocity Torque about centre

Two forces F F2 act on uniform rod of mass 2 kg and length 4 m placed on smooth horizontal surface as shown If the rod moves translationally with acceleration of 6 m s then F L 2 L 4

A box of mass 1 g is mounted with two cylinders each of mass 1 kg moment of inertia 0 5 kg m2 and radius 1m as shown in figure Cylinders are mounted on their control axis of rotation and this system is placed on a rough horizontal surface The rear cylinder is connected to battery operated motor which provides a torque of 100N m to this cylinder via a belt as shown If sufficient friction is present between cylinder and horizontal surface for pure rolling find acceleration of the vehicle in m s2 Neglect mass of motor belt and other accessories of vehicle regligible

vidiks 4 00 V 21 1 0 A uniform disc of radius 20 cm is performing pure rolling on a moving surface if its angular velocity is 5 rad s then find velocity of its centre of mass

ring of mass 2m and radius R is rolling on horizontal floor with speed of center of mass Vo A particle of m is connected to the ring on its perimeter The KE of system at the instant shown in the gure is O2mv m

A thin spherical shell m R translates without any rotation upon rough horizontal surface with centre m with velocity Vo friction appears which retards translational motion but causes the body to rotate At t the rigid body rolls without slipping 71 The distance covered by the shell from t 0 to t to 2 2 8 Vo 1 25 4 9 2 4 v 3 54 9 72 Work done by force of friction from t 0 to t to s 2 1 3 4 5 mv 4 25 t 0 mv 2 4 4 v 25 9 2 8 v 5 9 mv 2 5 t to 2 4 mv E 73 A solid cylindrical disc rolls down on inclined plane having inclination 60 with horizontal withou The initial acceleration of the topmost point of the disc is

question 3 Q 15 and 16 A thin rod of length L and mass m moves on smooth horizontal surface with speed voj in the direction of its length The end of the rod hits the end of second rod of same mass and length place angle to first one Two ends strick together after collision then C Vo 15 Angular velocity of system after collision about an axis passing through common centre of mass of system is 300 300 k A AL 2L 1 B B 310 A www D 16 Maximum speed attained by end A of system after collision 2 A 2 3 5 310 k C k 5L B 200 3 D D 14 X 3 5 300 2L k

34 A force F is applied to the homogeneous crate of mass m The coefficient of kinetic friction between the crate and surface is u Determine the minimum and maximum value h so that the crate will slide without tipping about its front edge or rear edge C A hmin B hmin C hmax b c b 1 mE c ub F b mg F mg F c ub C F Crate

A disc of radius R rolls and slips on a horizontal surface with linear velocity vi and angular velocity w k such that v Rw There is a particle P on the circumference of the disc which has velocity in vertical direction Angle made by line joining that particle to centre with downward vertical will be O sin 1 V Rw cos 1 sin 1 V Rw Rw V y d X D

A uniform rope of length I is held motionless on a frictionless hemisphere of radius r with one end of the rope at the top of the hemisphere The hemisphere is fixed on a horizontal floor The location from top end at angular position where maximum tensile force is developed immediately after the Rope is released

0 A man and mass m are initially situated on a diametrically opposite ends as shown in figure At some instant they start moving with constant speeds v and v The man moves in j direction and mass moves in a circle Find the linear momen tum of the mass with respect to the man as a function of time

A uniform thin rod of mass m length is hanged with the help of two identical massless springs of spring constant k as shown in figure Just after one of the spring is cut the acceleration of the other end of the rod will be E

22 A rigid lamina is rotating about an axis passing perpendiuclar to its plane through point U as shown in figure 5 50L 5m 370 4m The angular velocity of point B w r t A is A10 rad s B 8 rad s 3m A ya RW 4x4 40 10rad s C 6 rad s D 0