Center of mass and momentum Questions and Answers

A chain lying on an absolutely smooth table half of it hanging over the edge of the table as shown in figure a The time it takes to slip off the table is affected if two equal weights be attached one to each end as shown in figure b a t time taken to slip in situation a t time taken to slip in situation b figure a M T figure b 2 t tb 1 t t 3 t tb 4 cannot be determined M

A rigid body consists of 3 particles of masses 3 units 5 units and 2 units located at the points the points 1 0 1 2 1 3 and 2 2 1 respectively Find the moments of inertia about i the y axis and ii the z axis

4 A light rod of length has point masses m and m attached to its 2 ends The moment of inertia of the system about an axis perpendicular to the rod and passing through its centre of mass is 1 2 3 m m m m m m 2 m m m m m m 1

4 A 4 XA 4x 4 compartment The track is frictionless The centre of 15 There are some passengers inside a stationary railway 15 79361 42 340 fam of the 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 bourC and C will move with respect to the ground neither C nor C will move with respect to the ground I 1 3 C will move but C will be stationary with respect to the ground I 4 C will move but C will be stationary with respect to the ground 31 27 2 xo m x tg 3 V A 4 Space for Rough Work effe auf feet and 3RT TE ti 1 C 3 C 2 CC 3 C 4 C 4 A Cf C of 9 the velocity of the

on the line joining the particles 4 none of the above 3 A particle of mass 3m is projected from the ground at some angle with horizontal The horizontal range is R At the highest point of its path it breaks into two pieces m and 2m The smaller mass comes to rest and larger mass finally falls at a distance x from the point of projection where x is equal to 3R 2 1 3 4 SR 4 3R 2 4 3R 4 03 3m fira a faz mi faca fera um R i ga 2 fam are in a foxx Biar I ML 4A 3R 4 1 5R 3 4 Space for Rough Work 8 ML MK NX 4 X fe F M L KJ MXK so the distance 4 3R 2 4 3R some dista move willL LOLYMPIADS I KVPY 1

www princeeduhub com 12 A bomb initially at rest explodes by it self into three 12 equal mass fragments The velocities of two fragments are 3 1 2 m s and 1 4 m s I The velocity of the third 1 21 21 3 21 21 fragment is in m s 2 27 23 C 4 21 21 13 13 A stone of mass m moving with a uniform speed v suddenly explodes on its own into two fragments If the fragment of mass m is at rest the speed of the other fragment is m v I m m m NEET P DTS 24 05082021 13 Imt fahiaker F 3 i 2 at at ate ce 1 21 21 3 21 21 V E h the

A metal ball hits a wall and does not rebound 25 whereas a rubber ball of the same mass on hitting the wall the same velocity rebounds back It can be concluded that I T 1 metal ball sufferes greater change in momentum 2 rubber ball suffers greater change in 1 momentum 3 the initial momentum of metal ball is greater than the initial momentum of rubber ball 4 both suffer same change in momentum 60 1 3 af 3 frand feel a 1 2 fa fe 3 res antes d C 4 Space for Rough Work

low sphere 9 Two spheres A and B of masses m and m respectively collide A is at rest initially and B is moving with velocity v along x axis After collision B has a velocity in a direction perpendicular to 2 V the original direction The mass A moves after collision in the direction 2012 Pre a Same as that of B b Opposite of that of B c 0 tan 1 2 to the x axis d 0 tan 1 2 to the x axis Holl

Test 1 Code A A ball collides with horizontal smooth ground with a speed of 30 m s Coefficient of restitution Magnitude of velocity of ball after collision is 642 m s 2925 m s 60 30 m s sala 4 241 2 3256 m s m s

turning to the tational force 2011 Pre ts the earth ojected m rest and Or 39 A ball moving with velocity 2 m s collides head with another stationary ball of double the mass If the coefficient of restitution is 0 5 then their velocitie in m s after collision will be 2010 Pre a 0 2 b 0 1 c 1 1 d 1 0 5 40 An engine pumps water through a hose pipe Wate passes through the pipe and leaves it with a velocit

A person of mass mis standing on one end of a plank of mass M and length L and floating in water The person moves from one end to another and stops The displacement of the plank is 1 3 Lm m M M m Lm 2 Lm M m 4 LM m M

Four identical spheres each of radius a are placed on a horizontal table touching one another so that their centre lie at the corner of a square of side 2a position of the centre of mass is a a a b a 2 a 2 c 3a 0 d 2a a

In a gravity free room a man of mass m is standing at a height h above the floor He throws a ball of mass m vertically downward with a speed u Find the distance of the man from the floor when the ball reaches the ground

al Exam HW September 26 2021 Problem 8 A small particle with positive charge q 3 75 x 10 C and mass m 7 00 x 105 kg is moving in a region of uniform electric and magnetic fields The magnetic field is B 4 00 T in the z direction The electric field is also in the z direction and has magnitude E 60 0 N C At time t 0 the particle is on the y axis at y 1 00 m and has velocity v 35 0 m s in the x direction Ignore gravity Y Part A VAX 8 of 8 Find the 2 3 and z coordinates of the particle at t 0 0200 s Express your answer in meters to three significant figures Enter your answers numerically sepa by commas Consta

A father 60 kg and his daughter 20 kg are both at rest on a frictionless ice pond The father lifts a 1 kg ball and throws it to his daughter with horizontal speed 5 ms the daughter catches it Then the speed of father is 1 12 m s the speed of daughter is 1 4 m s the speed of father is 5 59 m s the speed of daughter is 5 21 m s

A wedge with a mass of 10 kg is at rest on a horizontal frictionless surface A block with a mass of 5 0 kg is placed on top and slides down the incline also startin from rest The surface of the wedge is rough At one instant the vertical component of the block s velocity is 3 0 m s and the horizontal component is 6 0 m s that instant the velocity of the wedge is 3 0 m s to the left O 3 0 m s to the right O 6 0 m s to the right O 6 0 m s to the left 5 kg 10 kg E Jh

A ball of mass m approaches a wall of mass M m with speed 4 m s along the normal to the wall The speed of wall is 1 m s towards the ball The speed of the ball after an elastic collision with wall is A 5 m s away from the wall B 9 m s away from the wall C 3 m s away from the wall D 6m s away from the wall

An elevator platform is going up at speed of 20 m sand during its upwards motion a small ball of mass 5 g falling in downward direction strikes the platform with speed 5 ms w r t ground and rebounds perfectly elastically The speed with which ball will rebound is O 25 m s 1 O 35 m s 1 40 m s 1 O 45 m s

A 50 kg man stands on a 150 kg cart whic moves horizontally with speed 3 m s on a smoot floor The man jumps horizontally on to anothe stationary cart of mass 175 kg What will be th common velocity of the man and the second ca if the first cart now moves with speed 1 5 m s the same direction 1 5 m s 3 2 5 m s 2 7 5 m s 4 1 66 m s

An elevator platform is going up at speed of 20 m s during its upwards motion a small ball of mass 5 g falling in downward direction strikes the platform with speed 5 m s w r t ground and rebounds perfectly elastically The speed with which ball will rebound is 25 m s 1 35 m s 1 40 m s 1 45 m s 1

00 A ball falls vertically on to a floor with momentum p and then bounces repeatedly the coefficient of restitution is e The total momentum imparted by the ball to the floor is a p 1 e c p 1 e 1 e b 1 Pe 1 e 4 P 1 1 e

3 In a Youngs double slit experiment the width of one of the slit is three times the other slit The amplitude of the light coming from a slit is proportional to the slit width Find the ratio of the maximum to the minimum intensity in the interference pattern a 1 4 b 3 1 c 4 1 d 2 1

same mass and radius are reported as I M L of thin circular ring about its diameter 12 M I of circula to disc an Screenshot Captured perpendicu 13 M I of sold cylinder about its axis and I4 M I of solid sphere about its diameter Then

A non conducting solid sphere of mass m and radius R having uniform charge density p and p as shown in figure It is then placed on a rough non conducting horizontal plane At t 0 a uniform electric field E E N C is switched on and the solid sphere starts rolling without sliding The magnitude of frictional force at t 0 is 2pxR E K Find the value of K III 111 X x 53 x xx x x

On to a sphere of radius R 2 and density p2 with centre at C2 a second solid sphere is moulded with density p radius R and centre C Find the force experienced by a point mass m at point P at a distance y from the combination as shown P1 P m R C P2 C

There particles are located at coordinates x y as follow m1 1 0 kg is at 1 0 m2 1 0 kg is at 2 0 and m3 2 0 kg is a at 0 2 Find the center of mass of the three particles with respect to the point 1 1

A bomb moving in certain direction suddenly explodes into three identical pieces which fly off with equal speed Two of the three pieces go in the same direction while the third one goes perpendicular to the other two If K and K are final and initial kinetic SKf energies of the system then fill in the OMR sheet K

An empty cylindrical beaker of mass m and radius r and negligible thickness has its centre of gravity at height h above its base To what depth should it be field with a liquid of density p so that system is most stable is given by a dm Fill a in OMR sheet Given m 10 kg h 1m p r 40 kg m

An impulse of I30N sec is given at t 0 to 3 kg block attached with 2 block with the help spring in natural length Initially the system is at rest and all surfaces are smooth Fin velocity of centre of mass at t 5 sec 2kg k 5 N m ooooooo 3kg

House Hot 4 Two objects of masses m 200 gm and m 500 gm possess velocities v 101 m sec and v 3i 51 m sec just prior to a collision during which they become permanently attached to each other Calculate a the velocity of the centre of mass b the finat momentum of the combination in the laboratory frame and c the initial and final momenta in the centre of mass frame d What fraction of the initial total kinetic energy is associated with the motion after collision

32 A body of mass 8 kg is hanging from another body of mass 12 kg The combination is being pulled up by a string with an acceleration of 2 2 m sec The tension T will be 12kg T 8kg ta 1 260 N 2 240 N 3 220 N 4 200 N 32 1 4 Km hr 3 12 Km hr 8 kg E l oels 2 19 211017 st 1 260 N 2

A particle of mass m moving with horizontal speed 6m s as shown in figure If m M then for one dimensional elastic collision the speed of lighter particle after collision will be u 6 m s m U 4 m s M A 4m s in original direction B 4m s opposite to the original direction C 2m s opposite to the original direction D 2m s in original direction

Two blocks A and B of masses 1 kg and 2 kg connected by light spring are placed on a rough horizontal plane as shown in the figure The coefficient of friction between the blocks and the surface is 0 4 Initially the spring is relaxed What minimum constant force F in N has to be applied in horizontal direction to the block A in order initiate sliding of B

2 Five faces of a homogeneous cube of mass m 4 0 g are painted in white reflects all wavelengths and one face in black absorbs as well as radiates wavelengths and the cube is placed in vacuum in free space at a very low temperature near absolute zero Initially when the cube is at rest it is given Q 900 J of heat As it cools down due to heat radiation it starts moving slowly Estimate its terminal speed Speed of light is c 3 108 m s

A chain of length is placed on a smooth whose some part is horizontal and some part is on quarter circular of radius R in the vertical plane as shown Initially the whole part of chain lies in the circular part with one end at topmost point of circular surface If the mass of chain is m then work required to pull very slowly the whole chain on horizontal part is R OR downloaded from allaboutnotes com m 79R sin A gR 2 7gR cos 2 79 sin gR

Two elastic balls of masses m and m are placed on top of each other with a small gap between them and then dropped onto the ground What is the ratio m m for which the upper ball ultimately receives the largest possible fraction of the total energy my 8 m

Two skaters initially at rest are 5 m apart They each have one end of a single rope and each pull on the rope with a force of 50 N for a period of 1 s One skater weighs 80 kg and the other weighs 45 kg Assume no friction between the skates and the ice ptions The two skaters meet at a distance of 1 8 m from the initial position of the heavy skater The two skaters meet at a distance of 3 2 m from the initial position of the heavy skater The relative velocity of the skaters when they meet is 125 72 m s The relative velocity of the skaters when they meet is 25 72 m s

A particle of mass m intially at rest is acted upon by a variable force F for a brief interval of time T It begins to move with a velocity u after the force stops acting F is shown in the graph as a function of time The curve is a semicircle 1 2 Question Type Single Correct Type 3 U U Force u TF 2m T 8m TTFOT 4m Fo t O Fot Time T

4 73 A block of mass 2 kg moving at 2 m s collides head on with another block of equal mass kept at rest a Find the maximum possible loss in kinetic energy due to the collision b If the actual loss in kinetic energy is half of this maximum find the coefficient of restitution 4 78 rest v ident on a toget com

ts 4 61 Two balls of equal mass moving in opposite direction have a head on collision with speed 6 m s If the coefficient of restitution is 1 3 the velocity of each ball after impact will be A 18 m s B 2 m s D 4 m s C 6 m s

and m2 4 50 Two particles of masses m in projectile motion have velocities and 2 respectively at time t 0 They collide at time to Their velocities become and 2 at time 21 while still moving in air The value of m v m v m m is A zero C 2 m m sto B m m sto D m m m gto

A smooth sphere of mass 1 kg is tied to a fixed point by an inextensible string and suspended from the roof Another identical sphere impinges directly on it with speed 5 m sec in a direction making an acute angle 30 1 with the string Co efficient of restitution is 2 1 2 Question Type Multiple Correct Type 3 A 7 30 B Speed of sphere B just after collision is 3 m s Speed of sphere A just after collision is 2 m s Impulse due to normal force between two spheres during collision is 6 N S Impulse due to tension in string during collision is 3 N S

Q 23 A ball of mass m 20 kg released from height h 10m falls on the Earth s surface The speed of the Earth when the ball reaches on the Earth s surface is 10 23 m s

person holding a rifle mass of person and rifle together is 100 kg stands on a smooth surface and fires 10 shots horizontally in 5 s Each bullet has a mass of 10 g with a muzzle velocity of 800 ms The final velocity acquired by the person and the average force exerted on the person are ms 0 08 ms 16 N b 0 8 ms 8 N 1 6 ms 16 N d 1 6 ms 8 N Wan NERT a 0 08 c 017

A solid cone is mounted on a solid cylinder of height h both made up of same material If the position of CM of combined system be at a distance h 4 below the center of base of cone the height h of the cone is h

A slender rod of length 6m forming an angle 60 with horizontal strikes a frictionless at A with its C M s velocity 7 m sec vertically down and no angular velocity Assum that the impact at A is perfectly elastic The angular velocity of the rod immediately after the impact is rad sec CM 7m sec YOUR ANSWER

A particle of mass m moves inside a bowl If the surface of the bowl is given by the equation z where a is a constant the Lagrangian of the particle is a 1 m r gar c m i r 0 r sin 4 gar 1 b m 1 a r 1 4 d m 1 a r r gar a x y

178 The stress strain graphs for two materials A and B are shown in the figure The graphs are drawn to the same scale Select the correct statement Stress P 0 0 Strain Material A Stress 0 0 Strain Strain Material B 1 Material A has greater Young s Modulus 2 Material A is ductile 3 Material B is brittle 4 All of these

In the figure m m 1 kg Block A is neutral while q 1C sizes of A and B are negligible B is released from rest at a distance 1 8 m from A Initially spring is neither compressed nor elongated 12 3 Equilibrium position of the combined mass is at x A VIN If collision between A and B is perfectly inelastic what is velocity of combined mass just after collision 6 m s 3 m s 9 m s A B C D 12 m s 2 B 13 C sja K 18 N m 5 smooth A x 0 D E 10 B x 1 8 m 7 NC x axis

A quarter sector of a uniform disc of radius R is shown in figure The coordinates of center of mass is y 1 Question Type Single Correct Type 2 R 3 2R 2R 3 3 2R 4R 3 3 4R 4R 3 3 R 4R 2R X