Center of mass and momentum Questions and Answers

3 Work Energy and Power Two blocks of mass m and 2m are moving towards each other along the same line with velocities 5v and v respectively If the collision is perfectly inelastic the energy lost in the collision is 5v V 1 5 mv E 2m 2 7 mv 33

Q 7 A ball hits a smooth the same speed as shown in diagram below The changes in the components of the velocity of the ball are TTT 1 1 1 010 1 A V 0 A V 0 2 A V 0 A V 0 X 3 A Vx 0 A V 0 4 AV 0 A V 0

All surfaces are smooth and the system is released from rest The block 2kg slides down an inclined surface by 10m Then the horizontal displacement of A wedge is 2 3 7 C block 1kg is m 2 6 3 7 m B block 2kg is 3 5 7 D block 1kg is zero m 2kg 60 4kg 1kg 30 20

Question No 21 Single Correct A A If particles of mass 1 kg 2 kg and 3 kg are placed at 1 0 1 2 2 3 and 1 3 0 Position of the centre of mass of the system is D 311 2 5 6 5 28 6 3 4 4 2 8 6 6 6 None

10 A rod with non uniform density is placed along x axis such that the end A of the rod is at the origin If the density of the rod increases as we move away from the origin then I and I rep resent the moment of inertia of the rod about A end points A and B 1 I IB LA 2 I IB 3 IA IB 4 None of these

Why not linear momentum since acc to Newton first law without external forces momentum does not change Q11 Internal forces can change for a system rakas ara ukalda Por faz ar A Kinetic energy but not linear momentum in an and B Linear momentum but not kinetic energy nu erau an afde m u vai n Linear momentum as well as kinetic energy 3 D Neither kinetic energy nor linear momentum Answer

Q8 Four point masses 1 kg 2 kg 3kg and 4 kg are located at the corner A B C and D respectively of a square ABCD of side 1m Then the radius of gyration of the system about AB as axis of rotation is a 0 3866 m b 0 8366 m c 0 6683 m d 0 6638m A B O C O D Other 1 poin

A ball of mass 1 kg bounces against the smooth floor as shown in the figure The approaching velocity is 25 m s and the velocity after hitting the ground is 15 2 m s then 1kg 25m s 53 50 15 2 m s A 0 has value 4 B impulse exerted on the ball is 5 5 3 2 Ns C impulse exerted on the ball is 35 Ns D Total Linear momentum of the ball is conserved

A ring of radius r is spun about its axis with an angular velocity in a horizontal plane A uniform magnetic field of magnitude B exists in the region in vertical direction The emf induced in the ring is Zero 1 2 Br Brzo

A particle of mass 6kg moving with a velocity of 10 m s collides with another particle of 3kg at rest initially If the coefficient of restitution is e 1 2 calculate loss in kinetic energy 1 75 J 3 125 J 2 100 J 4 200 J

For an inelastic collision the kinetic energy loss is the following 1 mm upp 1 e Happ 2 m m KE Lass where e coefficient of restitution v V u u a nd u app u approach U U

A particle of mass m and velocity collides oblique elastically with a stationary particle of mass m The angle between the velocity vectors of the two particles after the collision is in degree

Figure shows a man of mass m holding a ladder attached to a weight of mass M by a string supported by a light smooth pulley If whole system is at rest initially and man climbs up the ladder by a distance relative to ladder then the displacemen ml of centre of mass system is xM Find the value of x www m HOKI M

A rigid ball of mass m strikes a rigid wall at 60 and gets reflected without loss of speed as shown in the figure The value of impulse imparted by the wall on the ball will be a mV mV c 2 b 2 mV mV d 3 NET V 60 60 www

19 A glider of mass m 1 25 kg moves with a velocity of 3 62 m s on a frictionless level air track and collides with a second glider of mass m2 2 30 kg that is initially at rest After the collision the first glider is found out be moving at 1 07 m s in a direction opposite to that of its initial motion What is the velocity of m2 after the collision

If five particles of mass m are placed on the vertices of a square pyramid of side length a and height a as shown in the figure then find out the centre of mass for the given system m m a a m O m a m

A trolley filled with sand moves on a smooth horizontal surface with a velocity 10 m s A small hole is made at the base of it from which sand is leaking out at constant rate As the sand leaks out Smooth surface The velocity of the trolley increases till 20 m s The velocity of the trolley decreases till it stops The velocity of the trolley remains 10 m s The sand applies a horizontal force on trolley towards right while leaking

P From an inclined plane two particles P Q are projected with same speed at same angle one up and other down the plane as shown in figure Which of the following statement s is are correct P 0 0 0 A The particles will collide the plane with same speed B The times of flight of each particle are same C Both particles strike the plane perpendicularly D The particles will collide in mid air if projected simultaneously and time of flight of each particle is less than t

Whole mass of system is assumed to be concentrated at COM for calculation of moment of inertia Whole mass of system is assumed to be concentrated at COM for calculation of gravitational potential energy Whole mass of system is assumed to be concentrated at COM for calculation of linear momentum Whole mass of system is assumed to be concentrated at COM for calculation of kinetic energy

0 A light has amplitude A after coming out from polariser Angle between transmission axis o analyser and polariser is 60 Light passing through analyser has amplitude 1 2A 3 3A 2 A

A uniform thin circular disc of mass M and radius R lies in the X Y plane with its centre at the origin Find the moments of inertia tensor What are the values of the principal moments of inertia Find the principal SEA axes

m m In the above figure are the surfaces are smooth m is at rest m is given velocity as shown For which of given value of m will the number of collision between m and m is only 1 coefficient of restitution 1 and all surfaces are smooth SolveLancer Test 1 m 4 m 11 m 1 5 m III m 2m IV m 3 5 m a I II b II IV c III IV d II III CO a b C

Consider two parallel uniform rods parallel to y axis each of mass m and length 7 Velocity of centre of mass of each rod is 2voi and the angular velocity is w A particle R of same mass m is moving with velocity voi parallel to the velocity of centre of mass of each rod as shown On the basis of above information choose the correct match Given vo lw 2 4464 93 uz fur AA 4c 03 2 A A GWAIA M H yc hu R Try uzme ug i GOTHIT ng i i THIT i v i H farfa 21 34 QAA H MM2 92 as gdaa mo P R S V B R List f 1 o y Jiefan 2v Q centre of rod AB AB 00 2 Kinetic energy of rod AB with respect to R RAB R Buf B D Buf Angular momentum of rod PQ with respect to the PQ Kinetic energy of rod PQ with respect to R PQ m u 3 X Angular momentum of rod AB with respect to R RAB List II 1 k mvol 6 2 k mvol 3 3 mvol k 2 4 mv 5 mv P 4 Q 1 R 5 S 2 P 5 Q 1 R 3 S 2 C P 5 Q 1 R 5 S 2 Correct Answer P 5 Q 2 R 5 S 2

A baseball pitcher delivers a fastball that crosses the plate at an angle of 6 93 degrees below the horizontal and a speed of 80 9 mph The ball mass 0 142 kg is hit back over the head of the pitcher at an angle of 35 67 degrees above the horizontal and a speed of 108 1 mph What is the magnitude of the impulse received by the ball

Two 500 g blocks of wood are 2 0 apa frictionless table A 10 g bullet is fired at 430 m s toward the blocks It passes all the way through the first block then embeds itself in the second block The speed of the first block immediately afterward is 5 2 m s Part A What is the speed of the second block after the bullet stops Express your answer with the appropriate units

31 A disc of mass m and radius R is rolling with angular speed on a horizontal surface as shown in figure The magnitude of angular momentum of the disc about point P here v is linear speed of centre of mass of disc y 1 mvR 2 3 mvR P D 2 4 O X 3mvR 2 mvR 4

A cue ball traveling at 7 39 m s makes a glancing elastic collision with a target ball of equal mass that is initially at rest The cue ball is deflected so that it makes an angle of 30 0 with its origina direction of travel a Find the angle between the velocity vectors of the two balls after the collision O b Find the speed of each ball after the collision cue ball m s target ball m s

Comprehension IV Two blocks A and B of masses 3 m and 2 m respectively are placed as shown in figure A 3 mmmmmmm Smooth Choose the correct answer 1 If block B is given velocity v 1 Maximum speed of A is ITE 2 Minimum speed of B is B 2m rightward then 4V 5 6m 3 Maximum elongation in spring is vok 4 Maximum compression in spring is V 6m

0 A bullet of mass m is fired from below into a bob of mass m of a long simple pendulum The bullet stays inside the bob and the bob rises to a height h The initial speed of the bullet will be a hg c M m 2h Vg M m b 2h M m d 2hg m M m M

A bag of mass M hangs by a long thread and a bullet mass m comes horizontally with velocity v and get caught in the bag Then for the combined system bag bullet IM 1 Momentum is mMv M m 2 Kinetic energy is Mv mv M m M 3 Momentum is 4 Kinetic energy is m v MV M m

One quarter sector is cut from a uniform circular disc of radius R This sector has mass M It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc Its moment of inertia about the axis of rotation is IIT JEE Screening 2001 a MR b 4 MR 90 c MR d 2 MR A thin wire of length L and uniform linear mass density p is

An explosion blows a rock into three parts Two pieces fly off at right angles to each other 1 kg with velocity of 12 m s and 2 kg with velocity of 8 m s If third piece flies off with velocity of 10 m s then its mass is 0 5 kg 1 5 kg O2 0 kg 2 5 kg

Three rigid rods are joined to form an equilateral triangle The two corners A 3 and B are pivoted and this assembly is kept in a vertical plane If M 10 1 1m and nail at B is removed what is instantaneous reaction at hinge A M 1 M I B M 1 Vertical Plane kg

13 The surface mass density mass per unit area of a semi circular disc of radius R varies as t ax 7 where a is a constant vector along positive x axis and is position vector with respect to origin It is kept on smooth horizontal surface with flat surface in contact with surface Now force F is applied in such a way that it moves translationally kf R 16 without any rotatic SRation The value of his then find value of k THE

A shell at rest at the origin explodes into three fragments of masses 1kg 2kg and m kg the 1kg and 2kg pieces fly off with speeds of 5ms along axis and 6 ms along y axis respectively If the m kg piece flies off with a speed of 6 5 ms the total mass of the shell must be B 5 kg C 3 5 kg A 4 kg D 4 5 kg

The areal mass density of a circular disc of radius R is given as a Por where x is the distance from the centre and po is a constant Its moment of inertia about an axis perpendicular to its plane and passing through its edge is 16 POTT RO

Two balls collide with each other and bounce as shown in the figure What is the final speed of the 700 g ball if the 900 g ball has a speed of 15 cm s after the crash 700 g 30 cm s 30 50 cm s 900 g

Two discs A and B of mass m 2 kg each are connected by a light rod of length 1 m These discs are placed on a smooth horizontal 3 m s hits disc B as shown in the figure The coefficient surface Another disc C of mass 2m 4 kg moving horizontally with velocity Vo of restitution is 12 2m m B m The velocity of A just after collision is zero Loss of energy after collision between B and C is 4 5 J Initial Impulsive tension of string at the time of collision is zero Angular velocity of rod just after collision is 3 rad s

A ball of mass m moving with a velocity v v 2g1 1 is the length of the string the bob of a pendulum of the same mass at rest which is hanging vertically with the string If the collision is perfectly inelastic the height to which both will rise is given by C B D

3 Consider a system of two particles having ma and m If the particle of mass m is pu m towards the centre of mass of particles thr a distance d by what distance would the pa of mass m move so as to keep the cent mass of particles at the original position slasdi ofc to signs ns mladi m m d a m m m a m my d b tidho orit of invent d d d

If the linear density mass per unit length of a rod of length 3m is proportional to x where x is the distance from one end of the rod the distance of the centre of gravity of the rod from this end is 2002 a 2 5m c 1 5m b b 1m d 2m 6

A solid sphere of radius R is placed on a smooth horizontal surface A horizontal force Fis applied at height h from the lowest point For the maximum acceleration of the centre of mass 221 2002 upo a h R b h 2R d Sa gol 82 8 c h 0 b d The acceleration will be same whatever h

If a mass m collides elastically with another identical mass at rest in oblique manner then after collision both the masses move at an angle of 1 30 2 45 0 In a conservative field the potential 3 60 4 90

Physics Sec 1 Maximum Marks 24 This section has 6 questions The answer to each question is a SINGLE DIGIT INTEGER ranging from 0 to 9 both inclusive Marking scheme o 4 If the correct integer is typed in the provided space o 0 In all other cases A wo skaters A and B weigh 40kg wt and 60kg wt respectively stand facing each other 5m apart on smooth horizontal surface They then pull a light rope stretched between them Find the distance in meter from A where they meet

Pls solve the following question by energy method A plank having mass M rests on the two identical spherical balls of mass m and radius R The plank is connected to springs and further these springs are connected to the walls as shown in figure Assuming the pure rolling of the spheres and no slipping will occur between plank and spheres 4 K A The angular frequency of small oscillation of the plank will be K k 7 10 M m K k 3 M m OR B The angular frequency of small oscillation of the plank will be 1 C The frequency of oscillation will be f 2 M D The time period of oscillation will be T 2 k K K 7 m 10 K k 7 M m 10

A geyser heats water flowing at the rate of 3 0 litres per minute from 27 C to 77 C If the geyser operates on a gas burner what is the fuel consumption rate if its heat of combustion is 4 0 104 J kg 1 15 7 g per min 2 15 10 g per min 3 14 39 g per min

B B 1 97 m s The system is initially at rest Block B has a mass of 4 kg The cart has mass of 10 kg The spring is attached to the cart and not the block The coefficier friction between the block and the cart is 0 5 The spring constant is 4800 N m and is compressed 0 1 m and then released What are the actual speeds o each immediately after the spring becomes undeformed Ignore friction during spring expansion C 2 13 m s B 3 16 m s C 0 771 m s B 2 21 m s B 2 93 m s C 1 17 m s C 1 21 m s C

o 1 partial marks for selecting each correct option o 2 In case if selected typed option is incorrect o 0 In case if no response is typed selected A body has its centre of mass at the origin The y coordinates of the particle may be all positive all negative all non zero positive for some cases and negative in other cases 27

Two particles P and Q initial at rest and 1 m apart P has a mass of 1 H and Q a mass of 3 kg P and Q repel each other and are set free to mo What is the separation between P and Q what is the separation in metre when P moves a distance 5 25 m from its initial position

A circular plate of uniform thickness has a diameter 56 cm A circular portion of diameter 42 cm is removed from one edge as shown in the figure The centre of mass of the remaining portion from the centre of plate will be A 5 cm C 9 cm 28cm 21cm B 7 cm D 11 cm