Rotation Questions and Answers

Water enters vertically and steadily into a sprinkler shown below and is discharged at a rate of 20 L s through ach nozzle Each nozzle has a discharge area of 2 cm Determine the torque required to prevent the sprinkler om rotating Assume p 1000 kg m for water 2 18 sm fo E 15 cm 1

4 Zero 151 neet prep A ring is rolling without slipping on a horizontal plane with velocity v and acceleration a The acceleration of point of contact is O 1 Horizontally towards right 2 Vertically upward 3 Vertically downward 4 Zero High Yielding Test Series Part Test 5 Half XIth Contact Number 9667591930 8527521718 Page A solid cylinder is rolling without slipping on a horizontal surface If VA VB and Vc are instantaneous velocities of points A B and C on the cylinder then which of the following is correct A 60

1 90 5 J 3 60 7 J 2 48 J 4 100 8 J As shown in the figure a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel disc of radius r and mass m When released from rest the bob starts falling vertically When it has covered a distance of h the angular speed of the wheel will be 1 2gh m r 3 XT T Ima m img 1 4gh 3

2 then of the into a of the own in 2 VA VB VC 3 VA VC VB 4 Vc VA VB 159 A uniform cubical block of side L rests on a rough horizontal surface with coefficient of friction A horizontal force F is applied on a block as shown If there is sufficient friction between the block and the ground then the torque due to normal reaction about its centre of mass is F 1 Zero 2 FL FL 3 2 4 3FL 0 2

The axis of rotation of a purely rotating body O Must pass through the centre of mass O May pass through the centre of mass O Must pass through a particle of the body None of these

Two uniform rods each of mass m 1 kg and length I 1 m are hinged at B and pivoted at C If a horizontal impulse FAt 7 N s is applied to the end A of the lower rod then find the angular velocity w in rad sec of the upper rod just after the impulse At is very small and rods can rotate freely w r t hinge and pivots 1 m B 1 m

8 A body is in pure rotation The linear speed v of a particle the distance r of the particle from the axis and the angular velocity wo of the body are related a e doinw V Thus r Xa a w x 1 r c 0 igale t pritiw allo sonil od eam to everige blloz Al b writo enla d is independent of r w d 0 nie 0 ito

4 it moves in a straight line A point P moves in counter clockwise direction on a circular path as shown in the figure The movement of P is such that it sweeps out a length s t 5 where s is in metres and t is in seconds The radius of the path is 20 m The acceleration AIEEE 2010 of P when t 2 s is nearly Ex B 20 m P x y A lai 4 14 m s

7 A diver in a swimming pool bends his head before diving because it a decreases his moment of inertia b decreases his angular velocity e increases his moment of inertia d decreases his linear velocity

A ring of mass m and radius R is acted upon by a force F as shown in the figure There is sufficient friction between the ring and the ground The force of friction force necessary for pure rolling is Ia F m R R MR a F 1 5 2 forward R 2 F 3 F fk cam Rf Ia forward

21 A solid cylinder is rolling without slippily velocity of its centre of mass v and angular velocity about its centre of mass won a horizontal frictionless surface as shown in figure If it collides with a frictionless vertical wall X then after collision its velocity and angular velocity respectively become I 1 IN 3 N 22 00 G X 2 V w

A solid cylinder of mass 50 kg and radius 0 5 m is free to rotate about the horizontal axis A massless string is wound round the cylinder with one end attached to it and other hanging freely Tension in the string required to produce an angular acceleration of 2 2 revolutions sis A 25 N C 78 5 N B D AIPMT 2014 50 N 157 N

Example 11 3 A sphere of aluminium of 0 047 kg placed for sufficient time in a vessel containing boiling water so that the sphere is at 100 C It is then immediately transfered to 0 14 kg copper calorimeter containing 0 25 kg of water at 20 C The temperature of water rises and attains a steady state at 23 C Calculate the specific heat capacity of aluminium

186 A rod of mass m and length 2R is attached to a circular ring of mass m and radius Ralong its vertical diameter as shown Horizontal force F is applied at top Friction is sufficient for pure rolling then friction force acting on the ring at the instant shown is N st Mgr 2 Ring m R Rod m F 20 N FR n

A 15 kg uniform disk of radius R 0 25 m has a string wrapped around it and a m 3 8 kg weight is hanging on string The system of the weight and disk is released from rest 1 When the 3 8 kg weight is moving with a speed of 1 4 m s what is the kinetic energy of the entire system K E 20 235 m Your submissions 20 235 X Computed value 20 235 Feedback Ann Submit 2 If the system started from rest how far has the weight fallen fall Submitted Saturday June 19 at 7 22 PM m Submit

Q 40 A wooden disc of mass M and radius R has a single loop of wire wound on its circumference It is mounted on a massless rod of length d The ends of the rod are supported at its ends so that the rod is horizontal and disc is vertical A uniform magnetic field Bo exists in vertically upward direction When a current I is given to the wire one end of the rod leaves the support Find least value of I d 2 A d 2 O Bo B