Center of mass and momentum Questions and Answers

View In English A piece of paper shown in figure 1 is in the form of a square Two corners of this square are folded to make it appear like figure 2 Both corners are put together c centre of square O If O is taken to be 0 0 the centre of mass of new system will be L 2 3 Correct Answer 4 COOR 2 0 1 2 0 72 0 2a O figure 1 2a O figure 2

Obtain the Lagrangian of a linear simple harmonic oscillator and the equation of motion in one dimension oln In a simple harmonic oscillator the particle is acted on by a force which is directed towards a fixed point

A thin light inextensible frictionless cord of length 1 wearing a small bead is tied between two nails that are in the same level a distance 0 5l apart Initially the bead is held close to a nail and released Find speed of the bead immediately after the cord becomes taut

A particle of unit mass collides elastically with ground at an angle 45 Then 10 2m s 1 3 777 Change in magnitude of linear momentum is 20 kgm s Change in magnitude of linear momentum is zero Magnitude of change in linear momentum is 20 kg m s Magnitude of change in linear momentum is zero rect Answer 2 3 tus unattempted I 459

V Two blocks of masses m and M are moving with speeds v and v v v in the same direction on the frictionless surface respectively M being ahead of m An ideal spring of force constant k is attached to the backside of M as shown The maximum compression of the spring when the block collides is M B V2 K m A V k mM C v V M m K m D None of above is correct K 000000 M

A small block having a mass m given a velocity u when it is on top of a horizontal board of sufficient length Mass of the board is 3m and is situated on a frictionless floor as shown The total work done by frictional force from the moment of projection to time t is M Drough 7 3m m 15 1 mu 2 smooth 30mu 3 mu 4 2 mu 16

A geometry consists of a square and a disc as shown in figure It is made up of an iron sheet of uniform density The y co ordinate of centre of mass of the geometry with respect to point O is 2a 4

A block m of mass 2 0kg is moving on a frictionless horizontal surface with a velocity of 1 0m s towards another block m of equal mass kept at rest as shown The spring constant of the spring fixed at one end of m2 is 100N m The maximum compression of the spring is 1 0m s

A body of mass 10 kg moving with velocity of 10 m s hits another body of mass 30 kg moving with velocity 3 m s in same direction The co efficient of restitution is 1 4 The velocity of centre of mass after collision will be Options 1 20 m s 2 40 m s 3 12 m s A

A wooden block of mass 0 9 kg is suspended from the ceiling of a room by a long thin wire A bullet of mass 0 1 kg moving horizontally with a speed of 100 m s strikes the block and gets embedded in it The height to which the block rises will be tg 19 m 4 Options

A sufficiently long plank of mass M is resting on a smooth horizontal plane A small block of mass m which is placed over the plank is given a velocity Vo relative to the plank If the coefficient of friction between the block and the plank is m then the loss of kinetic energy of the block until the relative slipping between the block and plank ceases will be 1 Proportional to u 2 Proportional to 1 3 Proportional to m M Vo VOS

An alternating electric field of frequency v is applied across the dees radius R of a cyclotron that is being used to accelerate protons mass m The operating magnetic field B used in the cyclotron and the kinetic energy K of the proton beam produced by it are given by 2012 B and K 2mn v R e B B 2 mv e 2 mv and K m TVR and K 2mn v R

A rock in outer space has a mass of 13 kg and is observed to be moving with a velocity of 6 5 3 2 4 8 m s You know that half a minute ago it experienced a force of 7 2 5 N for 1 5 seconds when a blast from the exhaust of the thrusters of your space shuttle affected it What was the rock s momentum before this happened 74 38 6 69 9 kg m s 10 5 3 7 5 kg m s 95 44 6 54 9 kg m s 84 5 41 6 62 4 kg m s

A 10 eV electron is circulating in a plane at right angles to a uniform field at magnetic induction 10 4 Wb m 1 0 gauss the orbital radius of electron is 1996 11 cm 18 cm 12 cm 16 cm

A coin is at center of board The mass of striker is double the mass of coin The initial direction of striker and final direction of coln are shown in figure Coefficient of restitution is e 0 5 Speed of striker before collision is 10 m s Mark the correct statements D F m 80 Speed of coin after collision 8m s Speed of coin after collis on 6m s Speed of striker after collision 2 21 m s Speed of striker after collision 6 m s

The Lagrangian of a particle of charge e and mass m in applied electric and magnetic fields is given by L mv e v e where and are the vector and scalar potentials corresponding to the magnetic 2 and electric fields respectively Which of the following statements is correct a The canonically conjugate momentum of the particle is given by p mv p 2m m c L remains unchanged under a gauge transformation of the potentials d Under a gauge transformation of the potentials L changes by the total time derivative of a function of b The Hamiltonian of the particle is given by H p ed

A small block A of mass m 2 kg is placed on a plank B of mass M 8 kg which is placed on a smooth horizontal surface The distance between the left end of the plank and its vertical wall is l 4 m The coefficient of friction between the block and the plank is 0 5 and collision between the block and the vertical wall of plank is perfectly elastic An initial velocity Vo is imparted to the block so that the block stops on the plank at its left enc after collision with the vertical wall Find the time in sec for which the block has moved relative to the plank Take g 10 m s A Vo M B

An Atwood system of masses m and 3m is initially at rest Mass of 3m is just in contact with ground A particle of mass m strikes block of mass m as shown in figure All collisions are inelastic and results in formation of unbreakable joints Choose correct options www F 124 3m 15 Speed of blocks immediately after collision is The magnitude of impulse due to tension in string just after collision of particle The block of mass 3m returns to original position intime Al FO 3mu 5 after com son of partic The maximum height reached by block of mass mapove on not position 50g

A smooth vertical rod is released form rest such that it is constrained to move vertically on a smooth wedge 0 45 When the wedge moves through distance x mass of rod mass of wedge m Contact force in options strictly refers to contact force between the rod and wedge only 0 Speed of the rod is Work done by contact force on the rod is mgx Work done by contact force on the wedge is m

A uniform disc of radius R is put over another uniform disc of radius 2R of the same thickness and densit The peripheries of the two discs touch each other Locate the centre of mass of the system from the cent of large disc

A square metal frame ABCD is made by joining 4 identical rods The frame is fixed to rotate about a horizontal axis through A ABCD lies in vertical plane The system is released with AB making 15 with horizontal Mass of each rod is 100g and length is 2m Consider g 10m s 0 13 B The maximum angular speed of frame is 3 rad s The maximum angular speed of frame is 6 rad s The hinge force on frame when i is having max ongular speed is 4 6N The hinge force on frame when it is having midu ongular speed is 64N

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

HIS SECOUNT COndins 20 questions Caur questommas 4 upons for correct answer Munupre Choice Questions CS Only one option is correct For each question marks will be awarded as UHOWS Full Marks 4 If correct answer is selected Zero Marks 0 If none of the option is selected Negative Marks 1 If wrong option is selected In the given figure table is smooth and pulley and string are ideal then acceleration of centre of mass of the two blocks system is m O 9 L x 2m

Two masses m and m start to move towards each 2 other due to mutual gravitational force If distance covered by m is x then the distance covered by m is 1 m x m m m x m m x m The total momentum of electrons in a straight wire 3 4 m x m m 1 X 3 mm 32 24 yerda za BRY UG m R AT m x m m m x m m x m m Inter T TRI TI NH 16 A SIRITefan m x 4

Two triangular plates of surface mass density 0 and 02 are joined together to form a rhombus of side a as shown y co ordinate of centre of mass is y co ordinate of centre of mass is x co ordinate of centre of mass is x co ordinate of centre of mass is 02 01 a 02 01 02 01 02 01 2 3 a 02 01 a 02 01 v3 02 01 a 02 01 2 3 60 01 5 60 X

ABCD is a rigid square wire frame carrying a steady clockwise current i with its centre at the origin At time t 0 the frame is at rest in the position shown in the figure Each side of the frame is of mass m and length A uniform constant magnetic field B is directed at an angle of 45 to the x xBi axis in the x y plane If the initial angular acceleration is the value of 12m X is D C B

Zero Marks A cannon of mass M 200 kg is positioned a top a narrow wall as shown It fires a ball of mass m 2kg horizontally across a plane Unfortunately the gunners forgot to lock the frictionless wheels of the cannon and it immediately rolls backwards off the wall landing distance 8 m from the wall as shown Neglecting air friction at what distance x in meters from the base of the wall does the ball land m

through a gas under the action of a constant force F The gas is kept at a very low pressure The speed of the plate u is much less than the average speed of the gas molecules Which of the following options is are true A B C Correct Answer The resistive force experienced by the plate is proportional to u Correct Answer The pressure difference between the leading and trailing faces of the plate is proportional to uv The plate continues to move with constant non zero acceleration at all times Correct Answer

A small ball of mass m at rest is struck by a large big ball with mass M 10m with an initial speed v a Could the following occur The big ball comes to a complete stop and the small ball takes off with speed 10v Explain your reasoning b Suppose instead that the objects stick together What is the final velocity of the combined object

A uniform cylindrical rod of length L cross section A and Young s modulus Y is acted upon by the forces as shown in figure The elongation of the rod is 1 33 1 2 3F 2 F 5 AY 3 F 2 4 F 3 F 5 AY 8 F 2F

Example A solid sphere rolls down on inclined plane from a height h as shown in figure Calculate time taken by sphere to reach the bottom Also calculate the minimum value of coefficient of friction necessary for rolling

12 If two balls each of mass 0 06 kg moving in opposite directions with speed 4 m s collide and rebound with same speed then impulse imparted to each ball by the other is 1 0 48 kg m s 3 0 53 kg m s 2 0 81 kg m s 4 0 92 kq m s

A particle of mass m moving with velocity u makes an elastic one dimensional collision with a stationary particle of mass m They are in contact for a very brief time T Their force of interaction F 1 increases from zero to Fo linearly in time and 0 decreases linearly to zero in further time magnitude of Fo is 2 3 mu T T2 2mu T mu 2T T 2 TIN 2 The

Moment of inertia of a uniform symmetric plate as shown in figure about x axis is 1 Moment of inertia of this plate about an axis passing through centre of plate O and perpendicular to the plane of plate is A 21 C 1 2 B I D 1 4 y axis 60 O x axis

5 Two masses mi 1 kg and M2 2 kg are connected by a light inextensible string and suspended by means of a weightless pulley as shown in the figure Assuming that both the masses start from rest the distance travelled by the centre of mass in two seconds is Take g 10 m s b a c 20 m 9 NIG 2 m d 40 9 1 m m 1 kg mi m 2 kg

Jos 2 27 Total momentum of electrons in a straight wire of length L carrying a current I is P if mass of electron is doubled keeping its charge constant and length of the wire is also doubled keeping current constant the new value of momentum will be nP so the value of n will be

11 A rod of length L is composed of a uniform length 1 L of wood whose mass is m and a uniform 2 1 length L of brass whose mass is mp The moment 2 of inertia I of the rod about an axis perpendicular to the rod and through its centre is L 12 a m m W c m m lo b m m 6 d m m

Three point masses are at the three corners of an equilateral triangle of side 50 cm The masses are m 3 kg m 2 kg and m3 5 kg You may put the masses in the corners of the triangle in any order Find the center of mass of the system What is the moment of inertia of the system about an axis which passes through the center of mass and perpendicular to the plane of the triangle

Three forces acting on a body are shown in figure To have the resultant force only along the x direction find the magnitude of the minimum additional force in newton needed F 4N 53 5N E 5N 37

Please Explain Question No 14 14 A rod AB slides on a V shaped wire with speed v as shown such that at any time OA OB I Magnetic field in the region is perpendicular downwards and has strength B induced emf in the rod is 60

Three identical metal balls each of radius r are placed touching each other on a horizontal surface such that an equilateral triangle is formed when the centres of the three balls are joined The centre of mass of the system is located at 1 horizontal suface 2 centre of one of the balls 3 line joining centres of any two balls 4 point of intersection of their medians

The centre of mass of a system of particles does not depend on 1 masses of the particles 2 Internal forces on the partices 3 position of the particles 4 relative distance between the particles

The centre of mass of a system of three particles of masses 1g 2g and 3g is taken as the origin of a coordinate system The position vector of a fourth particle of mass 4g such that the centre of mass of the four particle system lies at the point 1 2 3 is a i 2j 3k where a is a constant The value of a is 1 3 10 3 mic 2 5 2 2 4

5 In the figure shown the left block of mass 1 kg is struck sharply with an impulse J horizontal to the right The spring of stiffness 200 N m was initially in its natural state The floor has friction coefficient u 1 4 and the mass of the right block is 2 kg For the minimum value of J in Ns if the heavier block is to move at all 1 Fill in OMR mmmmm

A ball of mass 5 kg is suspended from a cord of length 0 5 m is attached to a cartA of mass 25 kg which slides freely on a frictionless horizontal track as shown in figure The ball is given an initial horizontal velocity 1 m s while cart is at rest Find The maximum vertical distance h in cm through which the ball will rise 25 kg A 5kgo ball

A uniform metal disc of radius R is taken and out of it a disc of diameter R is cut off from the end The 2 centre of mass of the remaining part will be Question Type Single Correct Type 1 2 3 R 10 from the centre R 15 from the centre R 5 from the centre

7 Four identical rods each of mass m and length I are joined to form a rigid square frame The frame lies in the xy plane with its centre at the origin and the sides parallel to the x and y axes Its moment of inertia about A the x axis isml B the z axis is m C an axis parallel to the z axis and passing through a corner is 0ml 10 D one side is 5ml

In the Hook s law experiment and according to the relation 7 41 k used spring is having 4 m M this means that the k effective mass zero effective mass zero effective mass zero None of the above

1 The probe Mangalyaan was sent recently to explore the planet Mars The inter planetary part of the trajectory is approximately a half ellipse with the Earth at the time of launch Sun and Mars at the time the probe reaches the destination forming the major axis Assuming that the orbits of Earth and Mars are approximately circular with radii RE and RM respectively Find the speed with respect to the Sun of the probe during its voyage when it is at a distance r R r R from the Sun M neglecting the effect of Earth and Mars Earth Sun RE Mars

Appliction 6 If a uniform rod of length L is bent at the mid point so that two halves are inclined by an angle 0 with each other then the shift in centre of mass is 0 CM C