Center of mass and momentum Questions and Answers

2 A smooth ball of mass m moving with a uniform velocity v strikes a smooth uniform rod AB of equal mass m lying on a frictionless horizontal table The ball strikes the rod at one end A perpendicular to the rod as shown in the figure The collision is perfectly elastic Some physical quantities pertaining to this situation are given in Column 1 while their values are given in Column II in a different order Match the values in Column ll and the quantities in Column l m m Column l A The ratio of final kinetic energy of ball its initial kinetic energy B The ratio of impulsion delivered to the rod to initial momentum of ball The ratio of angular momentum of rod about its centre of mass to the initial angular momentum of the ball about the centre of mass of the rodr D The ratio of final kinetic energy of rotation of the rod Column II e

NEET PHYSICS Q 94 The moment of inertia of a thin sheet of Q 94 mass M of the given shape about the specified axis is The axis is in the plane of sheet 1 12 3 11 Ma 45 All India Major Test Series Phase I II Major Test 28 22 03 06 2020 ft specified axis uta 2 Ma 12 4 2 1 Ma 1 74 7 12 3 Ma 1 Ma 45 2 Ma 12 4 Ma 12

body of mass M and moving with velocity u makes a head on elastic collision with another stationary body of m If A m M then the ratio f of the loss of energy of M to its initial energy will be 1 2 3 4 ect Answer 4 Answer 2 Is incorrect f A A 1 A f f f A 1 UA A 1 4A A 1

the moment of ng through the motion of the to be smooth king ball that the maximum 4 17 A ball of mass m moving at a speed v makes a head on collision with an identical ball at rest The kinetic energy of the balls after the collision is three fourths of the original Find the coefficient of restitution Ans ated

mass m on one end while another mass a ladder with a M on its other end as shown in the figure 2 Initially system is at rest The man climbs up with velocity Vo relative to ladder If all strings and pulleys are ideal then the velocity of centre of mass of this system is 1 3 4 mV 2M MV M m mVo M m M MV 7 M m m

uring a ballistic test designed to measure the muzzle velocity of a rifle a 7 90 g bullet is fired into a 6 20 kg wooden block of mass sitting on a table The block des 13 3 cm across the table after the bullet becomed embedded into it befroe it comes to rest The coefficient of kinteic friction between the table and the ock is 0 400 What was the speed of the bullet before it entered the block

the centre of a circular ice rink a 89 0 kg ice skater moving 1 85 m s north hits and grabs onto a 53 0 kg ice skater who had been traveling west at 4 70 m s the skaters hold onto each other and the rink has a 39 0 m diameter what is the amount of time for the skaters to reach the edge of the rink

asses are placed at co ordinates 1 1 2 2 and 4 4 respectively The position co ordinate of COM of system of three particles is 27 1 0 0 2 7 3 3 3 4 2 2 Consider a system of two identical particles One of the particles is at rest and the other has an acceleration a The centre of mass has an acceleration 2 0 2 NCERT Pg 146 4 1 Zero 3 a 4 2 a A thin uniform flat plate is in shape of L as shown The mass of lamina is 6 kg The position of centre of mass from point O INCERT Pg 147 1 2 1 1 NCERT Pg 146 10 a 2 1 Plate 5 6 2 mm Which relation regarding product of two vectors is incorrect NCERT Pg 151 1 x 0 2 a b c ab a c 3 axb a x 5 4 xb bx h The vector product of given two vectors A 31 41 5k and B 21 j k is INCERT Pg 152 1 91 13 11k 2 3 9 7 11K 4 91 7 11k The force acting on a particle is Find the torque of this force about origin if position vector of force is 7 3 5k m NCERT Pg 157 1 7 16 11k 3 16 11k 2 16 11k 4 9 11k

A ball of mass 1 kg is projected with a velocity of 20 2 m s from the origin of an xy co ordinate axis system at an angle 45 with x axis horizontal The angular momentum in SI units of the ball about the point of projection after 2 s of projection is take g 10 m s y axis is taken as vertical 1 400 K 2 200 3 300 tut 4 350 SH

why cant we use centripetal acc v2 2r GM 2R 2 BY THIS 2ND OPTION IS COMING AND ALSO BY FORMULA KE PE 2 2ND OPTION IS COMING WHY CANT WE USE BOTH THIS FO RMULA IN THIS QUE PLS EXPLAIN REASON DONT SEND SOLUTION The minimum and maximum distances of a satellite from the centre of earth are 2R and 4R where R is radius of earth If mass of the earth is M the maximum speed of satellite will be GM VR GM V2R 3GM 2R

A block m m kg strikes a stationary block m3 3 m kg inelastically Another block m 2m kg is kept on m3 Neglecting the friction between all contact surfaces Find the percentage decrease in kinetic energy of the system m m kg cm3 3m kg GDZY G4 THAM 1 m 2m kg a 1 ak zuh warte aut cht m3 ch aqua m AT A Guf glava h Magi

A particle of mass m strikes normally to a stationary wedge of mass 5m kept on the smooth horizontal surface as shown If the particle sticks to the wedge then loss in kinetic energy of the system during collision is W cu tef gur A 5 1 4ft hu aada de Cache AGU JAG 13 15 mv B mv m z adda Gesetz 30 5m

Three identical planks of uniform mass density and length are kept on each other as shown Plank 3 Plank 2 Plank 1 A B al maximum length of AB so that all the planks remain in equilibrium is Find a Assume all surfac 4 to be smooth Rotation RKH Sir 2013 RB EQ Used in JR CT 3 22 11 2015

In the given diagram shown all three rods are of equal length L and equal mass M The system is rotated such that rod C is the axis The moment of inertia of the system is 1 4ML 5 2 1 2 BL 2 A C 4ML 3 Gw 3 Ez f12

A segment of angle 8 is cut from a half disc symmetrically as shown If the centre of mass of the remaining part is at a distance a from O and the centre of mass of the original half disc was at distance d then it can be definitely said that A B C a d a d a d depending on a

3 13 From a uniform disc of mass M and radius R a concentric disc of about 4 Axes 1 and 2 are perpendicular to the disc and 3 and 4 are in the plane remaining angular disc I is the moment of inertia about axis 1 I about 2 13 about Axes 2 3 and 4 intersect at a common point Column I A I is equal to B L is equal to C I3 I is equal to D L 13 is equal to 21 32 Q 1 2 15 32 15 21 estions P R Column II S MR MR MR

A cubical container of mass m is placed on smooth horizontal surface as shown in figure A small ball of mass m is given velocity u 32 m s w r t ground perpendicular to wall of container at the bottom of container Coefficient of restitution of collision of ball with any of the wall is e 1 4 Calculate velocity in m sec of ball after 2nd collision with respect to container wall Side View um 2L Top View m

Two identical billiard balls strike a rigid wall with same speed as shown in the figure The ratio of magnitude of impulse imparted to the balls by the wall NCERT I XI Pg 98 1 2 3 U U 2 3 11 1 30 30 dical IIT JEE Sun

Three particles of equal masses are placed at co ordinates 1 1 2 2 and 4 4 respectively The position co ordinate of COM of system of three particles is 1 0 0 3 7 7 NCERT Pg 146 2 7 2 4 2 2

A glass slab ABCD is made of two different grades of 3 glass of refractive indices and of equal thickness and a ray PQ is incident on the face AB Trace the ray as it passes through the slab and find the angle of emergence and the angle of deviation Find the effective refractive index of the slab P 60 4 3 Type Text Add your responses H 3 2 Asked by 2241155 aesl id Standard X Stream Foundation Jul 14 2021 4 02 F B

For the setup shown below find the velocity of plank after collision The co efficient of restitution between ball and plank is 1 2 A 5 m s m 137 2m 10 ms 1 5 ms B 6 m s ve C 6 5 m s D 8 m s

A train is moving slowly at 2 m s next to a railway platform A man 1 5 m tall alights from the train such that his feet are fixed on the ground Taking him to be a rigid body the instantaneous angular velocity in rad sec is A 1 5 B 2 0 C 2 5 D 3 0

Four identical spheres each of radius 10 cm and mass 1 kg are placed on a horizontal surface touching one another so that their centres are located at the corners of square of side 20 cm What is the distance of their centre of mass from centre of either sphere a 5 cm c 20 cm b 10 cm d None of these

A body of mass 2 kg moving with a speed of 4 m s makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its initial speed The speed of the two body centre of mass is m s Then the value of x is ngo mathongo mathongo mathongo mathongo

A smooth uniform rod of length L and mass M ha two identical beads of negligible size each of mas m which can slide freely along the rod Initially the two beads are at the centre of the rod and the system is rotating with angular velocity about its axi perpendicular to the rod and passing through it mid point see figure There are no external forces When the beads reach the ends of the rod the angular velocity of the system is Bead Bead 1 2 1 2

angular momentum L If the frequency of mot is doubled and its kinetic energy is halved angular momentum becomes 1 2L 2 4L 3 L 2 Imo 2 2 L FW W Y L IX W

A small particle of mass m moving inside a heavy hollow and straight tube along the tube axis undergoes elastic collision at two ends The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure When the distance of the piston from closed end is L Lo the particle speed is v Vo The piston is moved inward at a very low speed V such I where dL is the dL that V Vo J L infinitesimal displacement of the piston Which of the following statement s is are correct Ich ha uum f farfa m Gw47 ci Yc ou gu atat fHR UP URTzel pu cidi ch u a am 3 yh Anda Ads hu yg Az uz d 6 fhul vilal Jach gu faxH GIT 3JHI yg m a gada fixa g 1 Mzca s agd g4 UM V 3 42 3R SA UGR V vod dL L fuzza ci 354 fazmua 21 a A4 33 H 47 as 2 2 V A The particle s kinetic energy increases by a factor of 4 when the piston is moved inward from Lo to Lo L a faza 0 1 dc 31 42 iz qfa huu vilal u i rau 3 v 4 i Juch 7 i Correct Answer B After each collision with the piston the particle speed increases by 2V zich cache alt Correct Answer L C If the piston moves inward by dL the dL particle speed increases by 2vd V e da fa hea 7 d hu tai D The rate at which the particle strikes the piston is

m1 m2 A head on elastic collision The masses slide without friction on the floor The figure shows the initial state m 3 kg ha velocity 3 m s and m 1 kg is stationary Determine the ratio of kinetic energies K K after the collision

A ball strikes a wall slanted at 45 as shown at a speed v and an angle 74 with respect to the wall It rebounds and moves vertically upwards away from the wall at a speed v2 Determine the coefficient of restitution e between the wall and the ball 45 V

If for a system of N particles of different masses m m2 my with position vectors 2 FN and corresponding velocities 2 respectively such that 0 then a the total momentum MUST be zero b the total angular momentum MUST be independent of the choice of the origin c the total force on the system MUST be zero d the total torque on the system MUST be zero

Common Data for Q 79 and Q 80 Consider a comet of mass in moving in a parabolic orbit around the Sun The closest distance between th comet and the Sun is b the mass of the Sun is M and the universal gravitation constant is G The angular momentum of the comet is a M Gmb b b GmM c G mMb d m 2GMb

For a particle moving in a central field a the kinetic energy is a constant of motion c the motion is confined in a plane b the potential energy is velocity dependent d the total energy is not conserved

14 Two billiard balls each of mass 0 5 kg moving in opposite directions with speed 6 m s collide and rebound with the same speed What is the impulse imparted to each ball due to the other Ahody of mass 25 kg is moving Ans 3 kg m s

29 Two steel balls A and B of mass 10 kg and 10 g rolls towards each other with 5 m s and 1 m s respectively on a smooth floor After collision with what speed B moves perfectly elastic collision 1 8 m s 2 10 m s 3 11 m s 4 Zero

Three thin rods each of mass m and length Lare joined to form as shown in the figure XQ P x S Moment of inertia of the system about an axis xx passing through rod PQ is 2ml 1 3 4mL En 2 ations mL 2 3mL

2mJ3gn m 6g Two identical balls each of mass 4 kg are moving towards each other with speeds 2 m s and 3 respectively They undergo head on perfectly elastic collision Then impulse imparted by one ball on othe 1 12 Ns 2 8 Ns 3 20 N

A bullet of mass 20 g pierces through a plate of mass M 1 kg and then comes to rest inside a second plate of mass M 2 98 kg as shown in the figure The plates are on a smooth horizontal surface and bullet moves along the surfaces It is found that the tow plates initially at rest now move with equal velocities Find the percentage loss in the initial velocity of the bullet when it is in between M and M Neglect any loss of material of the plates 3012 M M

A ball A moving with certain velocity along the positive x axis collides with a stationary ball B After collision their directions of motion make angles a and with the x axis The possible values of a and Bare 1 a 30 and B 45 2 a 90 and 120 3 0 and 30 4 a 45 and 0 X

A man A mass 60 kg and another man B mass 70 kg are sitting at two extremes of 2m long boa of mass 70 kg standing still in the water as shown They come to the middle of the boat Neglec friction How far does the boat move on the water during the process A 1 5 cm leftward 2 5 cm rightward 3 7 cm leftward 4 7 cm rightward B

A ball hits a smooth surface and rebounds with the same speed as shown in diagram below The changes in the components of the velocity of the ball are 30 sis eie TTTRITX 1 A V 0 A V 0 2 AV 0 AV 0 AV 0 AV 0 4 AV 0 A V 0 X 1 5

Suppose your teacher is showing a thought experiment in a gravity free space He struck a thin rod of M and length L at one end by a clay ball of mass m moving with speed v The ball sticks to the end of the rod Now to check your knowledge about rotational mechanics he asks you to find out the angular momentum of the clay rod system about the midpoint of the rod Select the correct answer O 90 A

C From a circular disc of radius R and mass 9M a small disc of radius R 3 is removed as shown in the Figure The new position of the centre of mass for the remaining disc will be Assuming positions of y direction to be positive and y direction to be negative 1 Point

1 A missile of mass 1 25 102 kg is fired from a plane of mass 4 75 103 kg initially moving at a speed of 2 60 102 m s If the speed of the missile relative to the plane is 1 06 103 m s what is the final velocity of the plane

There are two wires of linear mass densities A and 2A and the tension in them are T and 2T respectvely Which wire is supposed to be the denser medium for transverse wave propagation ONO 1st wire 2nd wire both are equally denser B

A cannon ball is fired with a velocity of 100 m s at an angle of 30 with the horizontal At the highest point of its flight it explodes into three equal fragments one going vertically upwards with a velocity of 50 m s the second one falling vertically downwards with a velocity of 50 m s The third fragment will be moving with a velocity of 1 300 m s in the horizontal direction 2 260 m s in the direction making an angle of 30 with the horizontal 3 300 m s in the direction making an angle of 30 with the horizontal 4 260 m s in the horizontal direction

A mass m is connected on either side with a spring each of spring constant k and k The free ends of springs are tied to rigid supports The displacement of the mass is x from equilibrium position Which one of the following is TRUE a The force acting on the mass is k k x b The angular momentum of the mass is zero about the equilibrium point and its Lagrangian is 1 mx k k x 2 2 1 mic c The total energy of the system is mi 2 my oooo m voor m 2 d The angular momentum of the mass is mxx and the Lagrangian of the system is x k k x

A particle of mass m is attached to a thin uniform rod of length a and mass 4m The distance of the particle from the center of mass of the rod is a 4 The moment of inertia of the combination about an axis passing through O normal to the rod is 64 a ma 48 c 27 48 2 mg 91 48 2 b ma 51 2 d ma 48 a 2 a 4

The Lagrangian of a particle moving in a plane under the influence of a central potential is given by 2 L m p 8 V r The generalized momenta corresponding to r and 0 are given by a mr and mr b mr and mr 0 c mr and mr d mr and mr

67 Two solid spheres each of radius R and mass m are initially at rest with respect to a stationary reference frame S The initial separation between the spheres is very large If the two move due to que mutual gravitational pull with what speed w r t the frame S will they strike each other esmosed ed lliw 169 noitsub 2 1 3 Gm 2Rb ass S 2Gm S re b Gm V Rab 8 SS 1 hichte 4 2 Gmca a

A satellite of mass m moves along an elliptical path around earth Its areal velocity is 1 Directly proportional to its mass 2 Inversely proportional to its mass 3 Independent of its mass 1 Directly proportional to square root of its mas