Rotation Questions and Answers

The disc is at rest at the top of a rough inclined plane It rolls without slipping At the bottom of inclined plane there is a vertical groove if radius R In order to loop the groove the minimum height of incline required is B C 15R 9R 4 5R 2 D Correct Answer Your Answer

is under pure rolling on a rough horizontal surface If the velocity of its center of mass is 10 m s Then its angular momentum about origin O will be yt 1 200 Nms M Vo X 2 300 Nms

force figure Then the ratio of linear acceleration and and the angular accelertion of the rod will be 1 2 1 3 4F 3m 3L 4 2F 3m L 6 In Q No 9 the acceleration of the end Q of the rod at the instant shown will be 3 2 F 3m 4 4 zero 2L 5

12 Assertion As wind flows left to right and a ball is spinned as shown there will be a lift of the ball Reason Decrease in velocity of air below the ball increases the pressure more than that above the ball

A circular disc of radius a with surface density of mass o Kr is under pure rolling on a rough horizontal surface such that the velocity of its center of mass is vo Then the ratio of its rotational and translational kinetic energies will be 1 1 2 2 2 3 3 3 5 4 5 7

A uniform thin cylindrical disk of mass M and radius R is attached to two identical massless springs of spring constant k which are fixed to the wall as shown in the figure The springs are attached to the axle of the disk symmetrically on either side at a distance d from its centre The axle is massless and both the springs and the axle are in a horizontal plane The unstretched length of each spring is L The disk is initially at its equilibrium position with its centre of mass CM at a distance L from the wall The disk rolls without slipping with velocity V Voi The coefficient of friction is u Figure 2d www d www x R Vo The net external force acting on the disk when its centre of mass is at displacement x with respect to its equilibrium position is A kx B 2kx C 2kx D 4kx

A machine of 250 kg mass is supported on springs of total stiffness 100 kN m Machine has an unbalanced rotating force of 350 N at speed of 3600 rpm Assuming a damping factor of 0 15 the value of transmissibility ratio is

r 2m is accelerating on a rough horizontal surface having coefficient of friction 0 2 Then the acceleration of its center of mass when a force of 45N is applied at its center of mass u 0 2 1 4 5 m s2 F 45N 2 5 5 m s 3 7 m s 4 6 m s In Q No 4 the angular acceleration of the circular disc in situation mentioned above will be 1 0 5 rad s 2 1 rad s 3 2 rad s 4 2 5 rad s

Two discs are in contact with each other The axis of both the discs has been fixed They can only rotate A force F has been applied tangentially on larger disc Assuming sufficient friction between contact surfaces The angular acceleration of smaller disc is 1 2 3 4 2F R m m 2F R m m F R m m F R m m m R a F R m

30 A metal sphere of radius r and specific heat S is rotated about an axis passing through its centre at a speed of f second It is suddenly stopped and 50 of rotations per its energy is used in increasing its temperature Then the rise in temperature of the sphere is f 1 m f s 2 f r 5S 10r S 8 a b C d 5 rf 14S

motor delivers constant power P to a cylinder of mass m and radius r which is free to rotate about it axis then the torque acting on the cylinder as a function of time will be 1 21 Pmr 6t Pmr 2 P V8tmr P

uniform boards tied together with the help of string are balanced on a surface as shown in the figure The coefficient of static friction between boards and surface is 0 5 The minimum value of 8 in rees for which this type of arrangement is possible is

A wheel of radius 20 cm and moment of inertia 1 kgm can rotate about its centre A string is wrapped over its rim and is pulled by a force F tangential to the rim of wheel If angular acceleration produced is 2 rad s2 ther the value of force F is 10 N 20 N 5 N 15 N

Two masses of 5 kg and 10 kg are connected to a pulley as shown What will be the acceleration of the system g acceleration due to gravity 1 q 2 g 5kg 10kg 0 O

17 Which of the following statements is correct a For a general translation motion momentum P and velocity need not parallel b For a general rotational motion angular momentum I and angular velocity in always be parallel c For a general translation motion acceleration a and velocity are always parallel d For a general rotational motion angular momentum I and angular velocity need not be parallel 18 A body is rotating with angular velocity b c d 23 Angu centr a ca b ca c ca d ze 24 The f positi

A uniform circular ring of mass m and radius R is placed freely on a horizontal smooth surface as shown in figure A particle of mass m is connected to the circumference of the ring with a massless string The particle is imparted velocity v perpendicular to length of string as shown If T is tension in the string just after the particle imparted velocity then 4T P 3R Acceleration of point P at this instant is T 2 3 2T 4 37

A solid sphere of mass m radius r undergo pure rolling inside a fixed vertical stationar circular track of radius R The sphere just completes vertical circle The normal at the lowe point of circular track is 34 a mg The value of a is

If the radius of a cylinder rotating about its axis is changing with time as R at such that its angular velocity o remains constant then the torque acting on the cylinder is proportional to mass of the cylinder m 1 t0 2 t 3 t 1 4 1 Two uniform rods of equal length but differe

A rod AB of length L and mass M is free to move on a frictionless horizontal surface It is moving with a velocity v as shown in figure End B of rod AB strikes the end of the wall Assuming elastic impact the angular velocity of the rod AB just after impact is A L B

are Two identical billiard balls of diameter 5 cm each moving with a speed of 3 m s roll without slipping towards each other on a horizontal rectangular U shaped trough that is sufficiently deep that the balls 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 How wide does the trough need to be approximately for balls to collide twice

As shown in the figure there are three masses m 2m and 3m kept at the vertices of an isosceles triangle Equal sides have length 1 1m and third side has length 2m Determine the moment of inertia of the system about line OX perpendicular to QR in the plane of P QR Take m 1kg 1 1m Q 2m 1m X Pam O A 3kg m P1 B 4kg m 1 1m 1m R 3m

QA 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 its plane with an angular velocity w Another disc of same thickness and radius but of 1 mass M is placed gently on the first 8 disc co axially The angular velocity of the system is now

QA uniform rod of length L is free to rotat in a vertical plane about a fixed horizontal axis through O The rod is allowed to rotate from its unstable vertical position Find the angular velocity of the rod when it has turned through an angle 0 A 0

Answer all questions Each carries 4 mark 5 A rotational K E of a particle rotating about a certain axis is 16J Calculat the angular moment of the particle about the same axis of rotation if the M I about its axis of rotation is 2 Kg m 2

M I about its axis of rotation is 2 Kg m 2 7 Calculate the MI of a cylinder of length 2 m radius 5 cm and density 8 x 10 3 Kg m 3 about its a axis of the cylinder b axis passing through the centre and perpendicular to its length

A dise weight W 100N and radius r 0 25 m supported at it acted up on by a constant couple of moment 6 Nm and a force of 50 N is applied to a cord wrapped around its periphery The angular velocity in rad s at two seconds after starting from rest is 5 Nm B 50 N

At a point beats frequency of n Hz is observed It means 1 medium particles at that point are vibrating with frequency n Hz 2 amplitude of vibrations changes simple harmonically with frequency n Hz at that point only 3 at that point zero intensity is observed 2n times per second 4 none of the above

a The diagram given below shows a uniform meter rule of weight 100 gf being balanced c a knife edge placed at the 40 cm mark by suspending a weight w gf at the mark 20 cr find 0 20 w gf 40 a 100 cm Metre rule to i the value of w ii the resultant moment and its direction if the weight w is moved to the mark 30 cm iii the position of another weight of 50 of to balance the rule in part ii

As shown in the figure two balls of same mass m are situated at the centre of a tube of mass M and are rotating with a uniform angular velocity 0 If the balls suddenly come to end of the tube the resultant angular velocity will be O M M 3m M M 6m O M 6m M 000 wh WO 1o 30 1 2 1 2 Marks 4 1

QA thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with an angular velocity w Another disc of the same dimension but of mass M 4 is placed gently on the first disc coaxially Find the angular velocity of the system

A weightless rod of length 2 carries two equal masses m one tied at lower end A and the other at the middle of the rod at B The rod can rotate vertical plane about a fixed horizontal axis passing through C The rod is released from rest in horizontal axis passing through C The rod is released from rest in horizontal position The speed of the mass B at the instant rod becomes vertical is O O A C 1 BOm 3gl 1 m

QA uniform rod of mass m and length I is free to rotate in the vertical plane about a horizontal axis passing through its end The rod is released from rest in the position shown by slightly displacing it clockwise Find the hinge reaction at the axis of rotation at the instant the rod tums through T

QA thin rod MN free to rotate in the vertical plane about the fixed end N is held horizontal When the end M is released the speed of this end when the rod makes an angle a with the horizontal will be proportional to see figure M N A B C D COS a COS a sin a a

A mobile system in the equilibrium condition is shown what is the ratio between weight of square and circle TA HII A 1 6 B 3 1 C 3 4 D 6 1 E 10 1 3cm 6 cm 4cm 1cm

A slender homogeneous rod of length 2L floats partly immersed in water being supported by a string fastened to one of its ends as shown in the figure The specific gravity of the rod is 0 36 The length of the rod that extends out of the water is KL Find the value of K 10

Two identical circular discs A and Beach of mass m and radius R are placed horizontally on a smooth horizontal surface with their centers fixed to the surface and touching each other as shown Now an impulse P is applied to the disc A as shown If there is no slipping between the discs the angular velocity of each disc will be

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 Br

radius R is rolling on a horizontal surface Find the angular momentum of the disc about an axis perpendicular to the plane of disc and fixed at point P to the disc P R 2 V

In the following figure the velocities are in ground frame and the cylinder is performing pure rolling on the plank velocity of point A would be A Question Type Single Correct Type 12Vc 2 2Vc Vp Vc Vp

Figure shows a solid sphere rolling without slipping on a horizontal surface Its radius is r mass is m and the velocity of its center is V Find the angular momentum about any point O on the horizontal surface along the line parallel to its velocity o V O 7 mvr

A solid uniform circular disc of mass m and radius R is spinning with angular velocity about its center of mass and is gently placed upon rough horizontal surface The angular velocity of rotation when pure rolling start 1 21 33 2w 2 3 N 2 3m

A metal rod of mass m can rotate about a horizontal axis O sliding along a circular conductor of radius a Fig The arrangement is located in a uniform magnetic field of induction B directed perpendicular to the ring plane The axis and the ring are connected to an emf source to form a circuit of resistance R Neglecting the friction circuit inductance and ring resistance find the law according to which the source emf must vary to make the rod rotate with a constant angular velocity w

With reference to figure of a cube of edge a and mass m which of ulo the following is the incorrect statement O is the centre of the cube a The moment of inertia of cube ma about z is I I 1 ma 2 D c Ix ly A X H E N Of C B G 2 The moment of inertia of cube about z is I F y

7 A spherical ball rolls on a table without slipping The fraction of its total energy associated with translation is 4 1 3 4 4 4 Afad god 2 5 3 2 x 2 2 4 27 7 20 1X9X4 8 20280 2 20

answer out or WHICH ONLY ONE IS correct 1 A uniform rod of mass m and length L is free to rotate in the vertical plane about a horizontal axis Which is passing through its end The rod is released from the rest in the position shown by slightly displacing it clockwise Find the hinge reaction at the axis of rotation at the instant the rod turns through 60 A 3 31 mg 16 B 68 3 3 31 mg 16 C 3 31 7 mg 16 73 1 D y 3 1

Various object of mass m and radius r having circular cross section are released from rest from an inclined wedge as shown in the figure Assume no slip condition unless stated g 10 m s 3 3 m 60 List I Object 1 Solid sphere II Disc III Hollow cylinder IV Hollow sphere m r 1 2 s ii iv Time to reach bottom S 25 10 List II S n K E List III translation K E rotation at bottom P 1 75 Q 1 5 R 2 5 S 2

A uniform rod of mass m is initially rotated about a vertical axis passing through its C M such that speed of both ends is v in opposite direction and placed gently on a rough horizontal surface If coefficient of friction between rod and surface is LI then rate of loss of kinetic energy just after the rod placed on surface is mgv 1 2 3 mgv mgv 2 4 2 mgv

A circular disc of mass 1 kg and radius 20 cm is rolling down a string without slipping as shown in figure If acceleration due to gravity at that place is 9 m s2 then the linear acceleration of the centre of mass of the disc is www 1 9 m s 3 3 m s infor Pe Enet 20 2 6 m s 4 1 m s

A dipole is placed at position a 0 0 in some external electric field Response of the dipole instantly is presented in Column l Column II is having the field and orientation of dipole Column l Q1 E 4xi P pli Q2 E 4xi P Plj Q3 Exi yi P Plj Q4 E xyi xj P Pli Q1 Q2 Q3 A1 A2 A3 A4 UU A5 n Column II A1 Dipole will experience net force A2 Dipole will experience net torque A3 Dipole will try to move towards origin A4 Dipole will try to move away from origin A5 Dipole will be in equilibrium

18 1 a b 2 c d 3 b d 4 a d A plate of uniform thickness is shown in figure It s center of mass is at origin O Now if the shaded area is removed the new position of the centre of mass is 2a 2a a a 21 2 3 4 1 3 3 4 29 6