Center of mass and momentum Questions and Answers

A ball of mass 100g dropped on the ground from 5 m bounces repeatedly During every bounce 36 of kinetic energy is loss Calculate i Coefficient of restitution ii Impulse given by the ball to the ground after third bounce iii Average force exerted by the ground If collision last for 250ms iv pressure exerted on ball by ground if contact area is 0 5cm 2

A canon shell moving along a straight line bursts into two parts Just after the burst one part moves with momentum 20 Ns making an angle 30 with the original line of motion The minimum momentum of the other part of shell just after the burst is 1 0 Ns

Two spheres of same radi but mass 2kg and 4 kg are moving toward each other They collide with restitution coefficient e 1 3 During collision the spheres deform and again reform to their original shapes Then A Zkg 4m s 2m s 4kg R A Magnitude of impulse each sphere experienced during deformation is 8 3Ns B Magnitude of impulse during reformation is 4 3Ns C Loss in kinetic energy of the system during deformation is 18 J D Loss in kinetic energy of the system during entire collision process is 16 J Answer BCD Solution 20 4 2 P and are velocities of A and B along the line of impact after collision 0 x 2 1 y m s and v m s

There are some passengers inside a stationary railway compartment The track is frictionless The centre of mass of the compartment itself without the passengers is C while the centre of mass of the compartment plus passengers system is C If the passengers move about inside the compartment along the track 1 both C and C will move with respect to the ground 2 neither C nor C will move with respect to the ground 3 C will move but C will be stationary with respect to the ground 4 C will move but C will be stationary with respect to the ground

2 b 0 45 kg m d 0 16 kg m 2 From a disc of radius R and mass M a circular hole of diameter R whose rim passes through the centre remaining part of the disc about a perpendicular axis is cut What is the moment of inertia of the passing through the centre NEET 2016 a 13 MR 32 c 9 MR 32 A disc and m b 11 MR2 32ros A d 15 MR 32 worla Taxi to

A 5000 kg rocket is set for vertical firing The exhaust speed is 800 m s 1 To give an initial upward acceleration of 20 m s 2 the amount of gas ejected per second to supply the needed thrust will be g 10 m s 1 185 5 kg s 1 2 187 5 kg s 1 3 127 5 kg s 1 4 137 5 kg s 1

A moving body of mass m collides head on elastically with a stationary body of mass 3 m Calculate the ratio of the momentum of the mass 3m after the collision to the momentum of mass m before the collision

A symmetrical square lamina of mass M has uniform semi circular plates attached to it on its four sides as shown in the figure Each plate has the same mass M and the side of a square is equal to a The moment of inertia of the system about an axis passing through the centre O perpendicular to the plane of the lamina is 25 A B 12 C 13 Ma 6 25 6 Ma Ma D none of these S CORRECT ANS D MO 10 B C

Calculate the moment of inertia a of a copper uniform disc relative to the symmetry axis perpendicular to the plane of the disc if its thickness is equal to b 2 0 mm and its radius to R 100 mm b of a uniform solid cone relative to its symmetry axis if the mass of the cone is equal to m and the radius of its base to R that in the case of a thin nlato of Demonstrate he following al

Figure shows a uniform rod of length and mass M which is pivoted at end A such that it can rotan in a vertical plane The free end of the rod B is initially vertically above the pivot and then releases As the rod rotates about A its angular acceleration when it is inclined to horizontal at angle is

et ball 1 has a mass twice that of ball 2 and ball 1 and ball 2 are located at 0 5 0 and 1 5 0 respectively a If you run the simulation with elasticity of 100 and initial velocities of ball 1 and ball 2 are 1 m s and at rest respectively i the velocities of the two balls after collision are v m s and v ii the momenta of the system before and after collisions are equal to m s kgm s and kgm s iii the kinetic energies of the system before and after collisions are equal to Joules Jules and

Two spheres are moving as shown Velocity v is such that spheres are at minimum separation when they touch each other Then A B 3 GM 28 R 6 GM 28 R C Speed of sphere A at the time of minimum separation is D Speed of sphere B at the time of minimum separation is 3 GM 7 R 6 GM 7 R M R 8R B

If a ball is rolling at a velocity of 1 5 m sec and has a momentum of 10 0 kg m sec what is the mass of the ball 2 What is the velocity of an object that has a mass of 2 5 kilogram and a momentum of 1 000 kg m sec 3 Tiger Woods hits 45 0 gram golf ball giving it a speed of 75 0 m sec What momentum has Tiger given to the golf ball

55 In two dimensional elastic collision which among the following are correct Momentum is always conserved of the system 2 Kinetic energy of the each particle remains same throughout 3 Momentum of colliding masses is conserved individually perpendicular to line of action if there is no friction 4 All of the above

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A man of mass m walks from end A to the other end B of a boat of mass M and length 1 The coefficient of friction between man and boat is and neglect any resistive force between boat and water Choose the correct statements A If the man runs at his maximum acceleration the acceleration of the boat is m M B Minimumtime taken by man to reach other end of the boat is g 2M M mug MI C Magnitude of displacement of center of mass of boat is M m D Velocity of CM of man and boat is zero

nelber bei 0 mol es 10 A child is standing at one end of a long trolley moving with a speed on a smooth horizontal track child starts running towards the other end of the trolley with a speed u the centre of mass of the system trolley child will move with a speed OOS 11 1 Zero 3 V 2 v u 4 v u AJUOMA GMA BUOR

8 Locate the centre of mass of arrangement shown in figure The three rods are identical in mass and length jume sqerie pri no abrageb 228m 10 y axis NOU eremos ort ta booslg 4p OS ig dose 1 NIN Ling out to learm ead bodks disl pisopi il on no altre ceem to ginen sit op 2 x axis 13 0

A uniform square plat abcd has a mass of 1 kg If two point masses each of 20 g are placed at the comers b and c as shown then the centre of mass shifts on the line X ing a W d N Y 2 OX

A uniform disc of diameter Ris put over another uniform disc of radius R of same thickness and density The peripheries of these two discs touch each other The centre of mass of the system from centre of big disc is Smaller disc C 0 Bigger disc RS 5

A body of mass M in the form of an inclined plane with a 450 angle of inclination lies on a horizontal plane A ball of mass m moving horizontally with velocity vo collides with the inclined plane After the impact the ball bounces vertically upwards and the inclined plane begins to slide without friction along the horizontal plane The velocity of the ball after the collision in its vertical travel is m 45 A VON mvo C M M m M M M m m B Vo V Mvo D m A body can rotate in a vertical plane at the C end of a string of length L The horizontal velocity imparted to the body in its highest position so that the tension in the string at

A block of mass M with the semicircular track of radius R rests on a horizontal smooth surface A cylinder of radius r slips on the track If the cylinder is released from rest from the top the distance moved by block when the cylinder reaches the bottom of the track is A B C R r m R r M m Correct Answer M M m A M M R r

Two identical uniform rods AB and CD eac h of length L are jointed to form a T shaped frame as shown in fig Located the COM of t he frame The COM of a uniform rod is at th e middle point of the rod Ans of this ques tion is L 4 Give me solution of this questio

A rod CD of length L and mass M is placed horizontally on a frictionless horizontal surface as shown A second identical rod AB which is also placed horizontally perpendicular to CD on the same horizontal surface is moving along the surface with a velocity v in a direction perpendicular to rod CD and its end B strikes the rod CD at end C and sticks to it rigidly Then D V speed of centre of mass of the system just after impact is the w angular speed of system just after collision is 3v 5L V speed of centre of mass of the system just after impact is the w angular speed of system just after collision is 5v 3L A L B L

Three identical spheres each of mass 1 kg are placed touching each other with their centres on a straight line Their centre are marked P Q and R respectively The distance of centre of mass of the system from P is 1 3 PQ PR QR 3 PQ QR 3 2 4 PQ PR 3 PR QR 2

28 A particle mass m is attached to a thin uniform rod of length a at a distance of from the mid point Cas 4 shown in the figure The mass of the rod is 4 m The moment of inertia of the combined system about an axis passing through O and perpendicular to the EAMCET 2013 rod is 91 2 ma b 32 a 27 10 ma C 2 Mass m q c 51 48 ma 112 d 64 48 ma

A 0 0427 kg racquet ball is moving 22 3 m s when it strikes a stationary box The ball bounces back at 11 5 m s while the box moves forward at 1 53 m s What is the mass of the box Unit kg Remember right is left is

Three particles of mass 1kg 2kg 3kg are placed at the corners A B and C respectively of an equilater triangle ABC of edge 1m Locate the centre of mass of the system Taking A as orgin AB as XY axis 3 4 7 m 12 m 3 i 2 12 m 3 2 3 12 2 m 4 12 3 m

A man of mass m is suspended in air by holding the rope of a balloon of mass M As the man climbs up the the balloon rope M m 1 Moves upward 2 Romains stationary 2 Moves downward 4 Cannot say fauore of side 2m Taking the point of

51 A projectile is projected tangentially from the surface of a planet of radius R If it is at a height of 3R at the farthest point of its trajectory then the velocity of projection Vo is given by acceleration due to gravity on surface g a vo 1 5gR c vo 1 6 gR b vo 0 5 gR d vo 2gR 3

33 What is the moment of inertia of solid sphere of density p and radius R about its diameter 105 a R p 176 176 105 c R P NIS I z w 2 FR 1 R 105 176 186 105 90 D b R p d R p UPCPMT 20 depends upon

Question No 9 Three solid spheres each of mass m and radius R are released from the position shown in fig The speed of any one sphere at the time of collision would be d d 0 Gm Gm 2 LR YOU

A disc has an angular velocity o about O The ratio of angular velocity of point P w rt A fixed to the ground and angular velocity of point Pw rt A fixed to the disc is A 2 B 3 R C 1 3 D 1 2

A chain of length I and linear density A hangs from a horizontal support with both ends A and B fixed to a horizontal support as shown The two fixed ends are close to each other At time t 0 the end A is released All vertical distances x are measured with respect to the horizontal support with the downward direction taken as positive A and B are initially at x 0 t 0 wwwww B A 1 2 t 0 wwwwwww Obtain the momentum P of the center of mass of the system when the end A has

A massive ball moving with speed v collides with a tiny ball which is initially at rest having a mass very much smaller than the mass of the first ball The collision is elastic then immediately after the impact the second ball will move with a speed approximately equal to Question Type Single Correct Type 1 V 2 2v 3 v 2

Two particles of mass 1 kg each are moving in opposite direction with speed of 6 m s and 4 m s and undergoes collision with coefficient of restitution Calculate loss in kinetic energy 1 in 2 75 1 4 75 2 4 300 8 3 4

B C As shown in the figure D is the centre of the circular base of a right circular solid con ABC whose vertical angle is 60 If the largest possible sphere is scooped out from the cone the centre of gravity of the remaining solid body lies at G Find the ratio of AG GD A 47 11 D 49 C 11 B D 48 11 50 11

7 From a circular disc of radius R a square is cut out with a radius as its diagonal The centre of mass of remaining portion is at a distance from the centre R R 4 2 2T 2 a b R 2 c R x 2 dl

Comprehension 1 One twirls a circular ring of mass M and radius R near the tip of one s finger as shown in the process the finger never loses contact with the inner rim of the ring The finger traces out the surface of a cone shown by the dotted line The radius of the path traced out by the point where the ring and the finger is in contact is r The finger rotates with an angular velocity The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact Figure 2 The coefficient of friction between the ring and the finger is and the acceleration due to gravity is g H Figure 1 R O Figure 2

3 4x 4 27 38 An electric fan has blades of length 30 cm as measured from the axis of rotation If the fan is rotating at 1200 r p m The acceleration of a point on the tip of the blade is about 1 1600 m s 3 2370 m s 2 4740 m s 4 5055 m s 38 3 47 To faccia 1 1600 m 3 2370 m

5 A kg block moving with 5 m s strikes a spring 2 of force constant 1000 N m attached to another 1 2 kg block at rest Kept on a smooth floor The time for which the rear moving block remain in contact with the spring will be Assume 10 5 m s 1 3 1 2 kg 1 31 81 S S K 1000 N m 1 000000000 2 2 1 20 4 1 10 kg S S

radius R No sand is to spill on to the surrounding area fls is the coefficient of static friction between sand parties then the choose the correct statement s The greatest height of sand pile that can be crated is fls R CORRECT ANSWER The greatest height of sand pile that can be created is R ls Minimum work required to create greatest height sand pile is 12 R pg When is the density of sand volume CORRECT ANSWER

Q 9 11 A uniform horizontal bar is located in a space where the strength of gravity g increases from left right Relative to the location of center of mass the center of gravity is located A B C D E at the extreme right end to the right at the extreme left end at the same position to the left

4 25 A ball of mass m moving with a velocity v undergoes an oblique elastic collision with another ball of the same mass m but at rest After the collision if the two balls move with the same speeds the angle between their directions of motion wil be A 30 C 120 B 60 D 90

A uniform T shaped object made of two thin rods of the same material with dimensions as shown in the figure lies on a smooth horizontal table A force F is applied to point P on the object such that it moves only translationally The distance of point P from point C is All quantities are measured in S l unit 04 10 00 C

Two identical balls B and C of same mass m are connected by a massless inextensible string and placed on a smooth horizontal surface as shown in the figure A third ball A of same mass m moving with a velocity vo collides with the ball B and after collision the ball A keeps moving in the same direction with a velocity Vo 5 o then the impulse applied by the string on the ball C during collision is kmvo Find the value of k m A 30 Cm B

The moment of inertia of a solid cylinder of mass M length 2R and radius R about an axis passing through the centre of mass and perpendicular to the axis of the cylinder is Options 5 MR 12 7 MR 12 5 MR 6 7 MR 6

25 A galvanometer having a resistance of 10 2 is shunted by resistance 1 2 if the total current i 2 A then which part of total current passing throug the shunt 1 11 A 20 3 A 2 1 A 4 4 0 5 A

19 A ball of mass m when dropped from certain height as shown in diagram strikes a wedge kept on smooth horizontal surface and move horizontally just after impact If the ball strikes the ground at a distance d from its initial line of fall then the amplitude of oscillation of wedge after being hit by the ball will be a md Mgo 1 M V2kh c d kg 068 Om b M k vooro d kMg 2h d d kg

Two equal particles are connected by an elastic string which is just taut on a smooth table the string being such that the weight of either particle would produce in it an extension a If one of the particles is projected with velocity u directly away from the other calculate the distance each particle would have travelled when the string first return to its natural length