Rotation Questions and Answers

Find wrong statement 1 Radius of gyration depends on mass of the object as well as distribution of mass II Radius of gyration depends only on mass of the object III Radius of gyration depends only on distribution of mass IV Radius of gyration depends on angular velocity of the object 1 I II III 3 I II IV 2 I II III IV 4 III IV

A sphere of mass m and radius r rolls on a horizontal plane without slipping with the speed u Now if it rolls up on a rough inclined plane the maximum height it would attain will be 1 3u 4g 3 7u 10g 2 5u 2g 4 u 2g

5 A disc of radius 0 1 m rolls without sliding on a horizontal surface with a velocity of 6 m s It then ascends a smooth continuous track as shown in figure The height upto which it will ascend is g 10 m s a 2 4 m c 2 7 m 6 m s b 0 9 m d 1 8 m

The moment of inertia of a uniform rod of length 20 and mass m about an axis xx passing through its centre and inclined at an angle a is 1 3 A m 3 me sin a cos a ia 2 mf 12 me DB sin a cos a

7 A spool of mass M and radius 2R lies on an inclined plane as shown in figure A light thread is wound around the connecting tube of the spool and its free end carries a weight of mass m The value of m so that system is in equilibrium is bronice si a 2M sin a c 2M tan a 2R a R Comun m b M sin a d M cos a lista A EI tue 100

12 A disc of radius r rolls without slipping on a rough horizontal floor If velocity of its centre of mass is then VO velocity of point P as shown in the figure OP r 2 and ZQOP 60 is a vo b Vo 2 c VO 7 Q O 60 2013 P d 3 Vo 2

3 A ball of radius r rolls inside a hemispherical shell of radius R It is released from rest from point A as shown in figure The angular velocity of centre of the ball in position B about the centre of the shell is A g 5 R r al a 2 c 2g 5 R r B b d 10g 7 R r 5g 2 R r

35 A spherical body of radius R is allowed to roll down on an incline without slipping and it reaches with speed vo at the bottom The incline is then made 5 smooth by waxing and the body is allowed to slide without rolling and now the speed attained is 400 The radius of gyration of the body about an axis passing through its centre is a R 3 5 c R b R 4 d R 5

15 A wheel is rolling without sliding on a horizontal surface The centre of the wheel moves with a constant speed vo Consider a point P on the rim which is at the top at time t 0 The square of speed of point P is plotted against time t The correct plot is R is radius of the wheel a c TV v2 4v 4v2 V2 TR 3TR 2V0 2V0 t b 4v2 d O pha 2v2 O TR TR Vo TR Vo t 2TR t

18 Four holes of radius R are cut from a thin square plate of side 4R and mass M The moment of inertia of the remaining portion about z axis is Y T a MR 12 3 10T 16 MR X b MR2 3 4 MR2 d 3 1 T CS 0 6 W

19 A wire of mass m and length 1 is bent in the form of a quarter circle The moment of inertia of this wire about an axis passing through the centre of the quarter circle and perpendicular to the plane of the quarter circle is approximately a 0 6 m b m1 c 0 2 m d 0 4 m

Two identical billiard balls of diameter 5 cm each moving with a speed of 3 ms roll without slipping towards each other on a horizontal rectangular U shaped trough that is sufficiently deep that the balls are clear of its base see figure The resulting instantaneous collision is perfectly elastic and during it each ball reverses its linear velocity through their angular velocities are not affected

A wheel whose moment of inertia is 12 kg m has an initial angular velocity of 40 rad sec A constant torque of 20 N m acts on the wheel The time in which the wheel is accelerated to 100 rad sec is Question Type Single Correct Type 1 72 seconds 2 16 seconds 38 seconds A 36 seconds

Consider two tangent axes to a uniform solid hemisphere as shown Let laB and Ico be moment of inertia of hemisphere about axis AB and CD respectively Then the ratio A 1 C 13 no AB ICD 28 13 D none of these B A

A thin sheet cut in the shape of a parallelogram of mass 500 g is shown in the figure Each side of the parallelogram is 6 m Find the moment of inertia SI units of the sheet about the axis PQ that coincides with edge AB of the sheet ns 3 No 45 B P A

A uniform thin bar of mass 6m and length 27 is bent to make a regular hexagon Its moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is B 6ml 1 C 4ml D m 12 A ns A 5 9 ml

BOXES ON TABLE PULLEY A system consists of three masses m m and m connected by a string passing over a pulley P The mass m hangs freely and m and m are on a rough horizontal table the coefficient of friction u The pulley is frictionless and of negligible mass The downward acceleration of mass m is Assume m ml m m a 81 gu 9 b 2gp 3 g 1 2 IN

116 The density of a rod is increasing from end A to B It is easier to set in rotation by 1 Clamping at end A and applying force Fat B perpendicular to rod 2 Clamping at mid of A and B and applying force F parallel to length of rod 3 Clamping the rod at midpoint of A and B and applying force F at a perpendicular to rod 4 Clamping the rod at B and applying a force F perpendicular to rod

A small mass slides down an inclined plane of inclination with the horizontal The co efficient of friction is Ho x where x is the distance through which the mass slides down and mo is a constant Then the distance covered by the mass before it stops is 1 2 3 2 tan 0 Ho 4 Ho tan 0 1 2 HO 1 tan 0

CAREER INSTITUTE 6 Three point masses each m are placed at the vertices of 6 an equilateral triangle of side a Moment of inertia of the system about the axis COD which passes through the mass at O and lies in the plane of triangle and perpendicular to OA is 7 1 ma 3 ma 4 ma BAM m m D The moment of inortin of a hody does not depend on SHM a you an fay vita da un 33447 CODE 1 ma 2 ma 3 ma 4 ma D m a faya a fer BAM m mai faviz ft COD

A wheel having moment of inertia 2 kg m about its vertical axis rotates at the rate of 60 rpm about this axis The torque which can stop the wheel s rotation in one minute would be 2 r a O 15 TT 15 N m N m b d T 12 TC 18 Nm N m

9 32 System of Particles and Rotational Motion A 3 m long ladder weighing 10 kg leans on a frictionless wall Its feet rest on floor 1 5 m from wall as shown What is reaction force of the wall NCERT Pg 162 50 3 vas N 3 m p 10 g 1 5 m 2 50 3N 3 100 3N 4 120 N 10 Which of the following statement is incorrect NCERT Pg 163 1 24 kg m 2 12 kg m 3 30 kg m 4 36 kg m 12 A cord of negligible mass is rim of flywheel disc with ma radius of 40 cm A steady applied to cord as show mounted on horizontal axis acceleration of wheel 40 1 10 33 rad s TE

4 36 kg m 12 A cord of negligible mass is wound round the rim of flywheel disc with mass of 15 kg and radius of 40 cm A steady pull of 50 N is applied to cord as shown The wheel is mounted on horizontal axis What is angular acceleration of wheel NCERT Pg 171 40 cm F 50 N 1 10 33 rad s 3 20 66 rad s A cord of negligible mass in wron 2 16 66 rad s 4 4 99 rad s bottom is Ring 2 Solid cylinder 3 Hollow sphere 4 Solid sphere 15 A car weighs 1800 kg its front axle and b centre of gravity is 1 The force exerted E wheels is g 10 ms 17500 N 3 9500 N 16 A ring circular of 100 kg It rolls pur

A solid sphere is in rolling motion In rolling motion a body possesses translational kinetic energy K as well as rotational kinetic energy K simultaneously The ratio K K K for the sphere is a 7 10 b 5 7 c 10 7 d 2 5

A uniform rod of length 3 m and mass 1 kg is free to rotate vertically about a fixed point A The rod is released from rest in the horizontal position The initial angular acceleration of the rod will be A O g 3g 2 g 2 g 3 B

A solid cylinder and a hollow cylinder both of the same mass and same external diameter are released from the same height at the same time on an inclined plane Both roll down without slipping Which one will reach the bottom first a Both together only when angle of inclination of plane is 45 b Both together c Hollow cylinder d Solid cylinder

6 One deterrent to burglary is to leave your front porch light on all the time If your fixture contains a 60 W bulb at 120 V and your local power utility sells energy at 8 cents per kilowatt hour how much will it cost to leave the bulb on for the whole month Show your work on the other side of this page

3 4 5 Paragraph for Question Nos 13 to 15 Two identical billiard balls of radius 5 cm and each of mass 1Kg moving with a speed of 3 ms roll without slipping towards each other on a horizontal rectangular U shaped trough that is sufficiently deep that the balls are clear of its base see figure The resulting instantaneous collision is perfectly elastic and during it each ball reverses its linear velocity though their angular velocities are not affected 200 more problems book I How wide does the trough need to be for the balls to collide twice A 3 cm B 5 cm C 15 cm D 10 cm Angular velocity of ball after collision is Assuming width of trough is least for second collision A 30 10 rad sec B 15 10 rad sec C 10 10 rad sec D 60 rad sec Minimum impulse of friction force so that second collision occure is A 3 Kg m s B 2 Kg m s C 1Kg m s D 10 Kg m s

Intrinsic semiconductor is electrically neutral 10 Extrinsic semiconductor having large number of current carriers would be A Positively charged B Negatively charged C Positively charged or negatively charged depending upon the type of impurity that has been added D Electrically neutral

Q 6 Two identical billiard balls of diameter 5 cm each moving with a speed of 3 ms roll without slipping towards each other on a horizontal rectangular U shaped trough that is sufficiently deep that the balls are clear of its base see figure The resulting instantaneous collision is perfectly elastic and during it each ball reverses its linear velocity through their angular velocities are not affected Answer When width 4 cm the balls will collide twice i Rate this question

more than 10 questions first 10 attempted questions will be considered for marking 36 A uniform rod of length L and mass M is held vertical with its bottom end pivoted to the floor The rod falls under gravity freely turning about the pivot If acceleration due to gravity is g what is the instantaneous angular speed of the rod when it makes an angle 60 with the upward vertical 3 1 2 1 2 3 3 2L 2 4 1 2 3g 38 2 4L 3g 2 1 2

3 48 A device consists of a smooth L shaped rod located in a horizontal plane and a sleeve A of mass m attached by a weightless spring to a point B as shown in figure 3 125 The spring length is and stiffness is equal to k the whole system rotates with a constant angular velocity o about a vertical axis passing through the point O Find the elongation of the spring How is the result affected by the rotation direction Figure 3 125 B

A disc of radius 50 cm is projected from the ground with its plane vertical such that the velocities of the topmost point A and lowest point B are VA 20i 10j m s V 101 10j m s at the instant of projection Here i and are unit vectors in the plane of the disc along the horizontal and vertically upward directions respectively The range of the disc is 4k meter Find the value of k

S A rod of man M and length L is at rest on a smooth horizontal surface A small man m strikes at one end of rod elastically and perpendicularly to the length of rod After collision small mass m comes to rest find m M 3 1 2 2 4 7 3 5 4 78

Two 4 kg blocks are attached to the ends of a 10 m light rod that can freely rotate about its center perpendicular to the length of the rod What is the inertia of this system What is the inertia of the system if the axis of rotation is located at one of the 4 kg blocks

When a disc is rotating with angular velocity a particle situated at a distance of 4 cm jus egins to slip If the angular velocity is doubled at what distance will the particle start to slip A I cm B 2 cm C 3 cm D 4 cm

A uniform sphere of mass mand radius rrolls without slipping down an inclined plane inclined at an angle 53 to the horizontal What is minimum value of coefficient of friction at which slipping is absent 7 15 8 21 11

A uniform rod of length l is pivoted at one of its ends on a vertical shaft of negligible radius When the shaft rotates at angular speed w the rod makes an angle with it see figure To find equate the rate of change of angular momentum direction going into the paper w ml 12 sin cos about the centre of mass CM to the torque provided by the horizontal and vertical forces FH and Fy about the CM The value of is then such that 0 Fv F H ExamSide Com

A rod of length L whose lower end is fixed along the horizontal plane starts to topple from the vertical position The velocity of the upper end of the rod when it hits the ground is Choose only 1 answer A 3gL

A rod is being rotated about an axis passing through an end and perpendicular to its length as shown in figure A bead is sliding along rod with constant speed v with respect to rod Acceleration and velocity of bead when it is at distance of from axis is a and v A a o ti C v vi col 0 1 7 B a ti 2voj D V o

A sphere is rolling without slipping on two horizontal and parallel rails that are not in the same level Distance between the rails is equal to radius of the sphere If speed of the centre of the sphere is u find greatest speed of a point on the sphere

In Figure a uniform beam with a weight of 60 N and a length of 3 2 m is hinged at its lower end and a horizontal force of magnitude 50 N acts at its upper end The beam is held vertical by a cable that makes angle 0 25 with the ground and is attached to the beam at height h 2 0 m What are a the tension in the cable and b the force on the beam from the hinge in unit vector notation L F

serted by the sphere on the track at the disc has a light inextensible string wrapped around a groove in the rim The free end of the 38 ing is held in the hand and the disc is released What is its linear acceleration

Figure a non uniform bar is suspended at rest in a horizontal position by two massless cords One the cord makes the angle 36 9 with the vertical the other makes the angle 53 1 with the vertical If the length L of the bar is 6 10 m compute the distance x from the left end of the bar to its center of mass 0 L com

A non uniform bar of weight Wis suspended at rest by two strings of negligible weight as shown in fig The angles made by the strings with the vertical are 36 9 and 53 1 respectively The bar is 2 m long Calculate the distance d of the center of gravity of the bar from its left end 36 9 VIK 2 m W 53 1

A uniform rod has mass m 2 kg and length l 13 m One end of the rod is pulled with a constant velocity of vo 34 m s along a frictionless horizontal floor in the negative x direction The other end is moving along a parabolic fixed curve The equation of the parabola is x 20y Find the angular velocity of the rod in rad s when the end point B is at 10 5 y axis B x 20y 10 5

m A ring of radius a and having mass m is placed on a smooth horizontal surface Two massless rigid rods AC and BD each of length a are attached to diametrically opposite points of the ring as shown in figure A particle of mass m moving with velocity v and another particle of mass 2m moving with velocity v as shown in figure strikes simultaneously the end A and B respectively and stick to rod Find the velocity of point B just after collision will be A Vo A C 23 48 43 48 Vo C al D B D 55 48 47 48 Vo Vo B VO 2m

A disc of radius R is rolling with or without slipping on a horizontal surface with instantaneous linear velocity V and instantaneous angular velocity P is a point on periphery of disc such that it s instantaneous velocity vector is vertical Orepresents the angular position of P as shown in figure is measured from upward vertical in anticlockwise sense The possible value s of 0 is are O T sin 0 sin 1 Re 1 V Ra T COS V Roo T cos V

3 A disc of mass M has a light thin string wrapped several times around its circumference The free end of string is 3 attached to the ceiling and the disc is released from rest Find the acceleration of the disc C m 3 g IM 3g 2 4 N 3 A B C D 4 D B C A Mt vac t ceeft aga are en forma and fer statens cu M 1 23 3 g m 2 4 M 32989 w N

b 4s C 2s 30 A uniform solid cylindrical roller of mass m is being pulled on horizontal surface with force F parallel to the surface applied at its centre If the acceleration of the cylinder is a and it is rolling without slipping then the value of F is a 2 ma b 3 ma 3 ma 2 g d 1s d 5 ma