Center of mass and momentum Questions and Answers

5 Figure 10 W18 shows two cylinders of radii r and r having moments of inertia I and I about their respective axes Initially the cylinders rotate about their axes with angular speeds and o as shown in the figure The cylinders are moved closer to touch each other keeping the axes parallel The cylinders first slip over each other at the contact but the slipping finally ceases due to the friction between them Find the angular speeds of the cylinders after the slipping ceases 1 1 Figure 10 W18 102 12

mig is If the centre of the mass of three particles is at rest and it is known that two of them are moving along different non collinear lines then the third particles must also be moving If the centre of mass of a system remains at rest then the net work done by all the forces acting on the system must zero If the speed of centre of mass of a system remains zero then the net external force acting on the system must be zero If the speed of centre of mass is changing then there must be some work being done by the internal forces on the system

4 Two particles of masses M and 4M are released from a 3 distance 10 metres from each other Find the point of collision from smaller particle 8 metres 2 2 metres 3 5 metres 4 6 metres

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 A 3R 4 B 2 5R 4 C D 3R

Determine the x and y coordinates of the centroid of the shaded area 125 mm O 125 mm Select one a 125 3 mm 70 2 mm O b 132 1 mm 75 8 mm O c 125 3 mm 82 4 mm O d 132 1 mm 67 6 mm 200 mm 200 mm 150 mm 60 mm

A uniform circular disc placed on a rough horizontal surface has initially a velocity v and an angular velocity as shown in the figure The disc comes to rest after moving some distance in the direction of motion Then Vo is rwo el 3 3 Q M 4 2 Vo AC f vozax

The moment of inertia of a triangle of base b and height h about the centroidal axis parallel to its base is Select one O a 1 36 bh Ob 1 3 b h Oc 1 12 bh C O d 1 3 h4

The linear density of a thin rod of length 1 m varies as 1 2x kg m where is distance from its one end placed at origin What is distance of centre of mass from this end 07 m 12 LO 60 05m Read More E

Two protons each of mass m and charge e are held at rest at distance 1 m apart in air The maximum velocity acquired by each proton after release is k 3 1 4 O e 2k m k 2 e 4 k m 2k

10 Two carts of masses m 3 174 kg and m 7 454 kg undergo an elastic collision Before the collision while the second cart is stationary the velocity of the first cart is v 5 73 If the final velocity after collision of the second cart is v 2 0 96 m s the final velocity m s of the first cart is

A block A of mass m is given a velocity vo towards another block B of same mass B is attached to an ideal spring of spring constant K A makes a head on perfectly inelastic collision with B Choose the correct option s K momm B m Smooth Vo LA m Time after the collision B attains its initial position again m for the second time is R 2 1 Time after the collision B attains its initial position again 2m for the second time is K

5 A body of mass m at rest breaks into three parts due to some explosion with masses in the ratio1 3 3 The two parts with same mass move in mutually perpendicular directions with a velocity of 15 m s The velocity of the remaining part will be A 5 m s B 45 2 m s C 5 32 m s D zero

2 28 A wedge of mass M 2 m rests on a smooth horizontal plane A small block of mass mo rests over it at left end A as shown in figure A sharp impulse is applied on the block due to which it starts moving to the right with velocity vo 6 m s At highest point of its trajectory the block collides with a particle of same mass mo moving vertically downwards with velocity v 2 m s and gets stuck with it If the combined mass lands at the end point A of the body of mass M length is cm Neglect friction take g 10 m s mo B 20 cm

12 If the density of material of a square plate and a circular plate shown in fig is same the centre of mass of the composite system 1 will be A inside the square plane B inside the circular plane C at the point of contact D outside the system D Kel

Two blocks of masses 3 kg and 6 kg are connected by an ideal relaxed spring and are placed on a frictionless horizontal surface The 3 kg block is imparted a speed of 2 m s towards left k 2 N m 2m s3kg mm 6kg List I P Q R The speed of 3 kg block is m s at time The speed of 6 kg block is time m s at The speed of 3 kg block is m s at time List II 1 2 3 TT sec 7 3 k 4 sec sec ho

Match the value of moment of inertia of structures in List I with corresponding results in List II List l List II P Q R 4 30 2R M R R 22 7 Uniform Rod M Uniform Semicircular Ring Axis is perpendicular to plane of ring Uniform disk of initial mass M from which circular portion of radius R is then removed M I of remaining mass about axis which is perpendicular to plane of plate 1 2 3 8MR2 11 MR2 12 13MR2 8 L

Three particles of same mass lie in x y plane The x y co ordinates of their positions are 1 1 2 2 and 3 3 respectively The x y co ordinates of centre of mass are 1 2 2 2 3 0

Choose only incorrect statement from the following A ful A The position of the centre of mass of a system of particles at any moment does not depend upon the internal forces between the particles effe fext B The centre of mass of a solid is never lies outside the body of the solid C A body tied to a string is whirled in a circle with a uniform speed If the string is suddenly cut the angular momentum of the body will not change from its intial value can go for for A Ruffa D The angular momentum of a comet revolving around a massive star remains constant over the entire orbit rg H n Enfera com

An electron beam accelerated from rest through a potential difference of 5000 V in vacuum is allowed to impinge on a surface normally The incident current is 50x103 mA and if the electrons come to rest on striking the surface the force on it is scacia a far fa A ford fa fa fazl dial BI 34TFTH STI 50 103 mA 727 32 24 i FORTHG A 5000 1 1924 10 N B 2 1 10 N C 1 6 10 N D 1 6 10 N Your Answer

3 2 4 1 A plate in the form of a semicircle of radius a has a mass per unit area of kr where k is a constant and r is the distance from the centre of the straight edge By dividing the plate into semicircular rings find the distance of th centre of mass of the plate from the centre of its straight edge 1 3a 2 2 a 2 3 3a 4 a n

3 the total momentum of the ball and the earth is conserved 4 the total energy of the ball and the earth remains the same A particle of mass m moving with a speed v hits elastically another stationary particle of mass 2m in a fix horizontal circular tube of radius r Find the time when the next collision will take place

A ball moving with velocity 2 m s collides head on with another stationary ball of double the mass If the coefficient of AIPMT 2010 restitution is 0 5 then their velocities in m s after collision will be 0 1 2 1 1 3 1 0 5 77 4 0 2

2v 2v A can of height h is filled with liquid of uniform density p If the liquid is coming out from the bottom then centre of mass of the can water in the can 1 first ascends and then descends 3 always decreases Taxa omiciranlar rings of linan V Belt Ba 2 first descends and then ascends 4 none of these 11 and of radius R each are joined to form a complete ring The

A solid iron ball A of radius r collides head on with another stationary solid iron ball B of radius 2r The ratio of their speeds just after the collision e 0 5 is 1 3 2 4 3 2 In 4 1 hora kis a constant and is the

1 1 00 J 2 0 67 J A thin rod of length L is lying along the x axis with its ends at x 0 and x L Its linear density mass length varies where n can be zero or any positive number If the position XCM of the centre of mass of the rod is plotted against n which of the following graphs best approximates the dependence of XM on n AIEEE 2008 with x as

Which of the following is incorrect 1 If centre of mass of three particles is at rest and it is known that two of them are moving different non parallel lines then the third particle must also be moving 2 If centre of mass remains at rest then net work done by the forces acting on the system must be zero 3 If centre of mass remains at rest then net external force must be zero 4 None of these statement is incorrect

An explosion blows a rock into three parts Two parts go off at right angles of each other These two are 1 kg first part moving with a velocity of 12 ms and 2 kg second part moving with a velocity of 8 ms If the third part flies off with a velocity of 4 ms its mass would be AIPMT 20097 1 5 kg 2 7 kg 3 17 kg 4 3 kg espectively The centre of mone

3 always decreases none of these Two semicircular rings of linear mass densities 2 and 2 and of radius R each are joined to form a complete ring The distance of the center of the mass of complete ring from its geometrical centre is 2R 3R 2 TC 2 3R 4 none of these ATC plank of length 1 which lies at rest on a frictionless horizontal surface

In the figure shown a hole of radius 2 cm is made in a semicircular disc of radius 6 cm at a distance 8 cm from the centre C of the disc The distance of the centre of mass of this system from point C is 1 4 cm 8cm 2 8 cm C 3 6 cm 4 12 cm of mass of the system of three rods of length 2a and two rods of length a as

A heavy truck moving with a velocity of 60 km h collides with a light drum at rest If the collision be elastic then the velocity of the drum immediately after collision will be AIIMS 2014 1 zero 2 60 km h 3 120 km h 4 uncertain 11

100 3 During the head on collision of two masses 1 kg and 2 kg the maximum energy of deformation is collision the masses are moving in the opposite direction then their velocity of approach before the collision is 1 10 m sec 2 5 m sec 3 20 m sec 4 10 2 m sec J If before

4 m m 2 m m 3 1 4 m v m v Two identical particles move towards each other with velocity 2v and v respectively This velocity of centre of mass is 4 zero 1 v 2 v 3 3 v 2 Consider the following two statements 1

SPECIFIC HEAT CAPACITIES OF GASES When an ideal diatomic gas is heated at constant pressure the fraction of the heat energy supplied which increases internal energy of the gas is 1 2 5 2 3 07 17 3 2 1 4

Suppose we have a small rocket with a full 120 liter fuel tank Fuel with a mass density of 1 kg liter is burned at a steady rate of 2 liters per second and can provide a constant thrust force of 5900 Newtons as it burns The rocket and fuel tank has a mass of 400 kg with no fuel in it The shape design of the rocket causes a resistance proportional to its velocity during flight of 2 v t where v t is in m s and the constant 2 for proportionality of resistance is 2 N m s Give a piecewise function for the force on the rocket over time and use the force equation to find a piecewise function for the acceleration of the rocket over time

Two particles of mass M and 2M moving as shown with speeds of 10 m s and 5 m s collide elastically at the origin After the collision they move along the indicated directions with speed v and v are nearly 2019 Main 10 April I M 2M 10 m s 30 45 5m s 30 45 2M M

Two particles of masses m and m2 are projected from the top of a tower The particle m is projected vertically downward with speed u and particle m2 is projected horizontally with speed The acceleration of centre of mass of the system is neglect air resistance same Question Type Single Correct Type 1 2 g downward m g m m2 downward

A particle of mass m as shown in figure Force F is being applied on trolley to move it on frictionless surface The angle 0 O O between string and vertical when particle is in equilibrium with respect to trolley is O DE tan tan tan wwwmmmmm m F 2mg F mg 2 F mg suspended by sless string a troll

A projectile of mass M is fired so that the horizontal range is 4 km At the highest point the projectile explodes in two parts of masses M 4 and 3M 4 respectively and the heavier part starts falling down vertically with zero initial speed The horizontal range distance from point of fringe of the lighter part is A 16 km 2013 C 10 km B 1 km D 2 km

The period of revolution of planet A around the sun 8 times that of B The distance of A from the sun i how many times greater than that of B from the sun 1 4 2 3 3 4 523 par 10 2 X 13

momentum of the system If one object within the system loses momentum it is gained by the other object within the system The combined momentum of both objects would be conserved Getting Ready Navigate to the Collision Carts Interactive in the Physics Interactives section of The Physics Classroom website http www physicsclassroom com Physics Interactives Momentum and Collisions Collision Carts physicsclassroom com Physics Interactives Momentum and Collisions Collision Carts Once the Interactive opens resize it as desired Select the Elastic Collisions option Experiment with changing the Mass and the Initial Velocity of the two carts Observe how the position of the carts along the track can be changed by dragging Learn to Start Pause and Reset the animation Path Collision 1 Blue Cart Initially at Rest Set the initial blue cart velocity to 0 m s Set the mass values to different values Run the simulation and record the mass and velocity values Before Collision Red Cart Blue Cart m s mRed Vred kg x kg Use mass and velocity values to complete the following momentum table Before Collision After Collision kg x kg x m s kg m s m s After Collision kg m s m s malec Valur kg x m s kg m s m s kg m s kg m s AMomentum

A block of mass 2 kg is free to move along the x axis It is at rest and from t 0 onwards it is subjected to a time dependent force F t in the x direction The force F t varies with tas shown in the figure The kinetic energy of the block after 4 5 s is 2010 F t 4N L 1 3s 4 5s

c 1 m s A body of mass m 3 513 kg is moving along the x axis with a speed of 5 00 ms The magnitude of its momentum is recorded as AIEEE 2008 a 17 565 kg ms 1 c 17 57 kg ms b 17 56 kg ms d 17 6 kg ms

Potential energy sinusoidal curve is shown graphically for a particle The potential energy does not depend on y and z co ordinates For range 0 x 2 maximum value of conservative force in magnitude is B Find the value of Here this force is corresponding to above potential energy and all units are in SI 6 3 0 U Joule B 1 2 1 3 2 2 x metre

mass M with a semicircular track of radius R rests on a horizontal frictionless surface A uniform cylinder of radius r and mass m is released from rest from the top point A The cylinder slips on the semicircular frictionless track The distance travelled by the block when the cylinder reaches the point B is A M R r M m B m R r M m 2g R r VM M m C 2g R r m M m M m R M D none m In the above question the velocity of the block when the cylinder reaches point B is 2g R r 2g R r A M B m C m D M M M m M M m R I C M JEE 1983

1 Two masses m and m2 are connected by a spring of spring constant k and are placed on a smo horizontal surface Initially the spring is stretched through a distance d when the system is relea from rest Find the distance moved by the two masses when spring is compressed by a distance d

Integer Type Questions 1 The magnitude of force f in Newton acting on a body varies with time t in millisecond as shown in the figure Find the magnitude of the total impulse in Ns of the force on the body from t 4 ms to t 16 ms IIT 1994 a 3 TON dioolov pdT F N 800 200 A B 0 EF 4 6 atbil b 4 d 6 D 16 t ms

Two particles A and B of masses m and 3m are moving along X and Y axes respectively with the same speed v They collide at the origin and coalesce into one body after the collision What is the velocity of this coalesced mass Hint X A m Bl3m Before collision y 14 4m After collision

A sphere P of mass m and velocity undergoes an oblique and perfectly elastic collision with an identical sphere Q initially at rest The angle 9 between the velocities of the spheres after the collision shall be 1 0 2 45 3 90 4 180

respectively Find the velocity of their centre of mass Two blocks of masses 5 kg and 2 kg placed on a frictionless surface are connected by a spring An external kick gives a velocity of 14 m s to the heavier block in the direction of the lighter one Calculate the velocity gained by the centre of mass binc forces rros 19 C M

A body A of mass M while falling 01 under gravity breaks into two parts a body B of mass 1 3 M 2 and a body C of mass M The centre of mass of bodies 3 a does not shift b depends on height of breaking c body B body B and C taken together shifts compared to that of body A towards