Center of mass and momentum Questions and Answers

13 0 The moment of inertia of a uniform semicircular wire of mass m and radius r about an axis passing through its centre of mass and perpendicular to its plane is 1 mr 2 3 mr 1 4 2 mr 4 mr 1 0 4

11 Two identical particles move towards each other with 11 0 yelocity 2V and V respectively The velocity of centre Chass is 505 i N 1 35 36 4m vo 1 V 3 V 72 2 V 3 2 10 6 N m 4 16 3 N m 11 V 4 zero 12 Af energy density of gas is 36 l m in an ideal gas then 12 fe the pressure of ideal gas is 24 N m 160 I I 3 40 N m 13 A scientist claims to have developed efficient engine while 13 working between 27 C and 327 C Then efficiency of engine will be Ab 100 bb X 300 Goo Energy 36 V 2 1 24 N m 3 40 N m a t at gerar sit 1 70 2 4 V 3 nf 27 C a 327 C 2 10 6 4 16 3 2 60 4 40

Seven homogeneous bricks each of length L are arranged as shown in figure Each brick is displaced with respect to the on in contact by L 10 Find the x coordinate of the centre of mass relative of the origin shown

A square of side L 2 is removed from one corner of a square sandwich that has sides of lengt L The center of mass of the remainder of the sandwich moves from C to C The displacemen 2 of the x coordinate of the center of mass from C to C is p L The value of p is 12

ALLEN Three identical blocks A B and C each of mass 9 2kg are kept on a smooth horizontal surface Block A is given a horizontal velocity 10m s towards B as shown in figure Block B and C are attached with a spring Find change in velocity of center of mass of system A B C if A collides with B elastically 10m s A 1 5 m s 3 20 m s B00000 C 2 10 m s 4 zero A B a C TH 2kg 8 ferat afara wa A an frangen AB A B C fra 10m s A 1 5 m s 3 20 m s Bars Afera m 10 m s f Bac fint afe en ufania B00000 C 2 10 m s 4 T

The impulse imported by an electromagnetic pulse of energy 1 5 10 2 joule when it falls normally on a perfectly reflecting surface is Onig one correct answer A B 4 x 10 10 kg mo s 2 10 10 kg m s C 10 10 kg m s

5 14 A stick of length lies on horizontal table It has a mass Mand is free to move in any way on the table A ball of mass m moving perpendicularly to the stick at a distance d from its centre with speed v collides elastically with it as shown in figure 5 138 What quantities are conserved in the collision What must be the mass of the ball so that it remains at rest immediately after collision M Figure 5 138

15 The wedge shown in the figure can slide without friction on a horizontal tabletop The mass of the wedge is M and its angle of elevation is a 30 A body of mass m slides down without friction along the wedge the path of the body makes an angle of 60 with the ground Find the ratio of the masses m M a M 6

Particle A of mass m 3 with another particle B at rest having mass m 20 m 2 2 C A 2 moving along the x axis with velocity v collides elasticall axis after the collision the change AX in de Broglie wavelength of particle A in terms o its de Broglie wavelength 20 before collision is A A2 m 3 If both particles move along the x 5 B A2 20 2 D AX 420

This question has multiple correct options A B C D the total kinetic energy of the system is always conserved Correct Answer the kinetic energy of the system before collision is equal to the kinetic energy of the system after collision the linear momentum of the system is conserved Correct Answer Correct Answer the mechanical energy of the system before collision is equal to the mechanical energy of the system after collision

A T shaped rod is placed in xy plane as shown in the figure If the rod is uniform and both parts are of equal length L and mass m then distance of centre of mass of the system from origin will be Ignore thickness of the rod Ay L 45 12 2 3 4 2 Pama H 2 4 4 3L 4 X

1 Centre of gravity C G of a body is the point at which the weight of the body acts 2 Centre of mass coincides with the centre of gravity if the earth is assumed to have infinitely large radius 3 To evaluate the gravitational field intensity due to any body at an external point the entire mass of the body can be considered to be concentrated at its CG 4 The radius of gyration of any body rotating about an axis is the length of the perpendicular dropped from the C G of the body to the axis Which one of the following pairs of statements is correct a 4 and 1 b 1 and 2 c 2 and 3 d 3 and 4 10101

Six point mass particles are is placed on horizontal surface such that arrangement form a regular hexagon as shown Calculate coordinate of center of mass of arrangement A 1 3 B 3 1 2 5m 1 0 0 4m A 2m 3m C 3 1 D 3 1

A 61 000 kg Rocky Mountain Double big rig is traveling at 0 5 m s About what velocity must a 730 kg compact electric vehicle have to achieve the same amount of momentum as the Rocky Mountain Double OB 365 m s O A 42 m s C 91 m s D 4 6 m s Rocky Mountain Double Small electric car

A particle of mass m moving with velocity vo on smooth surface collides elastically with uniform rod 4m 1 and comes to rest immediately Velocity of end A just after collision is m B Vo 3 Vo 2

34 A particle of mass 4kg moving with a speed s collides with a train moving in an opposite direction with a speed of 20m s If coefficient calculate the final speed of the 1 2 particle in m s 1 5 3 20 restitution e 2 15 4 35 Of

A rod non uniform mass distribution The mass increases from left end A to right end B It is easiest to rotate the rod about an axis ATTIT y Question Type Single Correct Type 1 Passing through A 2 Passing through B

Determine the angular momentum of a 70 g particle about the origin of coordinates when the particle is at r 4 3 m y 5 8 m and it has velocity 3 11 8 4k m s th Find the ar component Express your answer using two significant figures VAE DOCE

A uniform cylindrical rod of mass m and length 17 L is rotating with an angular velocity oo The axis of rotation is perpendicular to its axis of symmetry and passes through one of its edge faces If the room temperature increases by t C and the coefficient of linear expansion is a the change in its angular velocity is 1 2mat 2 coat 3 3 mat 4 wat 2 95 am 1 2coat 3 3 out a fa a for you 2 coat 4 a wat 2

3 The moment of inertia of a uniform cylinder of length and radius R about its perpendicu bisector is I What is the ratio e R such that the moment of inertia is minimum 1 3 2 w 2 4 1 3 2 201

8 The beam shown in the figure has negligible weight If the system hangs in equilibrium when W 400 N calculate the value of W Take sin 20 0 34 cos 20 0 94 0 7L 120 37 0 3L W 37 0 W

71 A man stands on a frictionless horizontal ground He slides a 10 kg block on the surface with a speed of 3 m s relative the ground towards a vertical massive wall The wall itself it moving towards the man at a constant speed of 2 m s The block makes a perfectly head on elastic collision with the wall rebounds and reaches back to the man 3 second after the throw At the moment the block was thrown the wall was at a distance of 10 m from the man a Find the mass of the man b Find the ratio of work done by the man in throwing the block to the work done by the wall on the block

7 A tennis ball of mass 150 g is thrown towards a wall at a velocity of 10 m s It is hit back in the opposite direction with a velocity of 20 m s If the ball is in contact with the wall for a period of 0 01 sec then the magnitude of the force acting on the ball is A 500 N B 150 N C 450 N D 300 N

There may or may not be mass at the centre of mass of an object The linear velocity of each point of rigid body rotating about a given axis is same The angular velocity of each point of rigid body rotating about a given axis is different I 0

43 A 10 eV electron is circulating in a plane at right angles to a uniform field of magnetic induction 10 Wb m 1 0 gauss the orbital radius c electron is 1 11 cm 2 12 cm 2 18 cm 4 16 cm

Two balls a and b having momentum 10kg m s and 17kg m s respectively are moving towards each other along straight line assu ming there is no external force are acting on 2 balls the final momentum of the 2 balls af ter collision along the direction of ball a is

2 A shell projected horizontally with a velocity of 165 m s from the top of a 15 m high wall explodes into two identical fragments in the air One of the fragments strikes the ground 1 5 s after the shell was projected at a distance of 240 m from the foot of the wall and 7 m to the right of the x axis Determine position of the other fragment at this instant Neglect air resistance and assume acceleration of free fall to be 10 m s

8 Two circular coils 1 and 2 are made from the same wire but the radius of the 1st coil is twice that of the 2nd coil What is the ratio of potential difference applied across them so that the magnetic field at their centres is the same 1 3 3 6 AIPMT Prelims 2006 2 4 4 2

View In English A composite rod comprising two rods of mass m and 2m and each of length I 1 m as shown in the figure Assume w 10 rad s and m 1 kg the KE of the rotating composite rod is 0 2 3 4 125 J 150 J 250 J 175 J Correct Answer 3 Status unattempted Add to Bookmark List www BONN D 64 m 2m k Peer Stat Unattempted 49 4 Correct 35 7 incorrect 14 9 Five charges of equal magnitudo placed at corners of a regular pontogen of Your ADSINGL A TEN View

amina is made by removing a small disc of diameter 2R from a bigger disc of uniform mass density and radius 2R as shown in the figure The moment of inertia of this lamina about axes passing through O and P is I and Ip respectively Both these axes are perpendicula Ip to the nearest integer is to the plane of the lamina The ratio Io 2R 0 2R P

A block of mass M 1 6 kg is lying on a plane incline at an angle of 0 37 to the horizontal The coefficient is 0 2 At the same time the block on the incline plane is released a shell of mass m 0 4 kg is fired into it horizontally with a speed of v 12m s and gets embedded How much will the block and the shell slide up the incline A 0 15 m C 0 10 m B 0 20 m D None of these M 0 3

Two blocks A and B of masses m and 2m respectively are connected by a spring of force constant k The masses are moving to the right with uniform velocity v 10m s each the heavier mass leading the lighter one The spring in between them is of natural length during the motion Block B collides with a third block C of mass m at rest The collision being completely inelastic Find minimum speed in m s of block A in the subsequent motion Question Type Single Correct Type 1 5

A disc of radius 20 cm mass 1kg is rolling with slipping on a flat horizontal surface At a certain instant the velocity of its center is 4 m s and its angular velocity is 10 rad s The lowest contact point is O Find angular momentum about any point on the ground at shown instant 10rad sec P 1 O Question Type Single Correct Type 0 60 4m s

Identify the correct statement s The centre of mass of an object must be within the object All the mass of an object actually concentrate at its centre of mass The centre of mass of an object can only be moved from rest if there is non zero internal force The total linear momentum of the system as observed from centre of mass frame of reference is alway

In the situation shown a man of mass 60 kg is initially located at the left end of 8 m long trolley of mass 240 kg The system is initially at rest over a smooth horizontal surface The man walks to reach the right and of the trolley at rest over a smooth horizontal surface The man walks to reach the right end of the trolley displacement of the trolley will be A 2 m C 2 4 m Smooth B 1 6 m D zero

In system of two particles it is possible Energy of system is conserved but momentum of system is not conserved O Energy of system is not conserved but momentum of system is conserved O Both energy momentum of the system are conserved Both energy momentum of the system are not conserved

1 x m are placed at the opposite ends of a rigid rod of length L and negligible mass perpendicular to it The position of point P on this The rod is to be set rotating about an axis rod through which the axis should pass so that the work required to set the rod rotating with angular velocity is minimum is given by wo m L m m L m x P 9 2 x m L x m L m m m2 the

20 A man of mass m is standing at one end of a trolley of mass M and length L placed at rest on a smooth horizontal surface The man starts moving towards the other end and covers distance L then distance moved by man w r t ground is 1 3 mL m M mL M 2 4 ML m M ML m

18 A particle of mass m makes a head on elastic collision with another stationary body of mass m If m rebounds with half of its original speed then m is 1 3 3 3 2 4 2

19 The centre of mass of a non uniform rod of length L whose mass per unit length is proportional to x where x is distance from one end 1 3 3L 4 J N x 0 2 4 x L 514 Space for Rough

A uniform spring is oriented vertically such that its top end is held fixed If the spring is stretched by pulling its bottom end downward a distance of 4 8cm how far does the spring s center of mass move 4 8 cm 2 4 cm it doesn t move at all not enough information given

4 horizontal direction 4 Shifted diagonally from initial position Father 80 kg and son 30 kg are sitting at one of the ends of a 4 m long boat 40 kg standing still on water They start to shift slowly Father stopped at centre of boat but son stopped at other end Neglecting friction with water how far does the boat move on the water during the process 1 1 87 m 2 1 5 m 3 1 25 m

A particle of mass 2m is projected at an angle of 45 with horizontal with a velocity of 20 2 m s After 1 s explosion takes place and the particle is broken into two equal pieces As a result of the explosion one part comes to rest The maximum height attained by the other part is Take g 10 m s 2 A 35 m B C D 40 m 15 m 20 m

A stationary light smooth pulley can rotate about a fixed horizontal axis A light rope passes over the pulley One end of the rope suppors a ladder with a man and other end supports counter weight of mass M Mass of the man is m Initially the system is stationary and the centre of mass of the counter weight is at a height h from that of the man as shown in the figure If the man starts to climb up slowly such that his center of mass reaches at the level with that of the counter weight A A Distance moved by counter weight relative to ground is w te ros B Distance moved by counter weight relative to ground is mh M m Mh M m C Distance moved by man relative to ladder is 00 D Distance moved by man relative to ladder is mh 2 M m mh M m M

2 25 1 Four holes of radius R are cut from a thin square plate of side 4R and mass M The moment of inertia of the remaining portion about z axis is 3 M MR 12 89 X 2 8 10T 3 16 MR2 2 2 4 g sing 3 E 4 4 3 6 MR MR

A particle strikes smooth floor with speed 20m s as shown in figure After the collision it performs a projectile motion having range 15m The coefficient of restitution for the collision is g 10 m s 20m s R 15m

Tal from a height h upon a fix horizontal plane and rebounds Il e is the coefficie of restitution the total distance travelled befo rebounding has stopped is 1 0 1 8 2 A 1 h 3 1 02 21 8 h 1

3 A child stands at one end of a boat moving with a speed v in still water If the child starts running towards the other end of the boat with a speed u the centre of mass of the system will move with a speed A day at 42 4ch dtall a r far fach auf d 1 v u 2 v 3 u 4 v u

Q18 A thin bar of length L has a mass per unit length 1 that increases linearly with distance from one end If its total mass is M and its mass per unit length at the lighter end is 20 then the distance of the centre of mass from the lighter end is 2014 Online a b c d 21373 L 2L M 3 201 4M AL 8M 201 4M 201 6M

A trolley of mass 300 kg carrying sand 200 kg in it is moving uniformly with speed of 40 km h on a frictionless track After a while sand starts leaking out of a hole on the track What is the speed of the trolley after entire sand is leaked out 1 24 km h 2 30 km h 3 66 km h 4 40 km h