Center of mass and momentum Questions and Answers

A block of mass M is placed on the top of a bigger block of mass 10M as shown in figure All the surfaces are frictionless The system is released from rest heat block of m 10 M 2 2 m Find the distance moved by the bigger block at the instant when the smaller block reaches the ground

5 An object of mass m and velocity 3v toward the east has a completely inelastic collision with an object of mass 2m and velocity 2v toward the north After the collision the momentum of the combined object has a magnitude of A 5mv B 7my C 10mv D 12mv E 15mv age Pu

R A disc of radius R is cut off from a uniform thin sheet of metal A circular hole of radius is now cut out 2 from the disc with the hole being tangent to the rim of the disc Find the distance of the centre of mass from the centre of the original disc tion

35 Six identical balls are lined in a straight groove made on a horizontal frictionless surface as shown Two similar balls each moving with a velocity v collide elastically simultaneously with the row of 6 balls from left What will happen DOOO 1 One ball from the right rolls out with a speed 2v and the remaining balls will remain at rest 2 Two balls from the right roll out with speed v each and the remaining balls will remain stationary 3 All the six balls in the row will roll out with speed v 6 each and the two colliding balls will come to rest 4 The colliding balls will come to rest and no ball rolls out from right

A B A body of mass m is moving with speed v makes a one dimensional collision with a stationary body of the same mass on a horizontal table They are in contact for a very small interval of time At The contact force between them varies as shown in the graph Neglect friction The coefficient of restitution for the collision will be F F 314 max 1 2At 3 t At

An astronaut hits a golf ball of mass m on the Moon where there is no atmosphere and the acceleration due to gravity is g 6 where g is the acceleration due to gravity on Earth Assume that the golf club is in contact with the ball time t Just after losing contact with the ball has an initial speed v directed at an angle above the horizontal for a club the 6 What is the magnitude of the average force exerted by the club on the ball during contact A my B mycose C D E mg 6 mg Cos 0 strausage p ish R vansain House No 1210 Obtain

A balloon has 8 gram of air The air escapes out from a small hole in the balloon at a uniform velocity of 7 cm sec If the balloon shrinks in 5 6 seconds then the average force acting on the balloon is 1 104 N 3 56 dyne 2 4 106 N 102 dyne

From a circular disc of radius R and mass M a R small disc of radius is removed as shown in 2 figure The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is D 5MR 32 13MR 32

Two point masses m and m at rest in gravity free space are released from distance d Find the velocity of the CM of the system at the time of collision of particles O Zero 02 3 O None Marks 4 1

A particle at rest suddenly disintergrates into two particles of equal masses which start moving The two fragments will Question Type Single Correct Type 1 2 3 4 move in the same direction with equal speeds move in any direction with any speed move in opposite directions with equal speeds move in opposite directions with unequal speeds

A particle of mass 2 kg is dropped from a height of 20m and rises to a height of 5m Calculate the change in momentum between before and after hitting the ground 1 30 kg m s 3 10 kg m s 2 Zero 4 60 kg m s

Two spheres A and B of masses m and m respectively collide A is at rest initially and B is moving with velocity v along x axis After collision B has a velocity in a direction perpendicular to 2 the original direction The mass A moves after collision in the direction AIPMT 2012 1 0 tan 1 V 2 0 tan 1 2 to the x axis 9 to the x axis 3 Same as that of B 4 Opposite to that of B

A thin plate A of mass m is affixed on the upper end of a spring lower end of which is affixed on the ground In equilibrium the spring is compressed by an amount xo Another thin plate B of mass 2m dropped from a height 3x above plate A hits the plate A moves downwards together with the plate A and after reaching a lowest position both the plates rebound upwards What maximum height above the initial position of the plate A will the plate B rise B

A merry go round made of a ring like platform of radius R and mass M is revolving with angular speed o A person of mass M is standing on it At one instant the person jumps off the round radially away from the centre of the round The speed of the round afterwards is a 2w b w d o c 0 2

Consider a non conducting ring of radius r and mass m and a particle of equal mass both at rest in free space The particle is on the axis of the ring and far away from the ring An amount of positive charge is uniformly distributed on the ring and the particle is given a positive charge q The particle is imparted a velocity u towards the centre of the ring Find maximum speed the ring can acquire during the subsequent motion Electrostatics 12 23 0

A uniform rod of length is released from rest such that it rotates about a smooth pivot The angular speed of the rod when it becomes vertical is 1 2 14 Question Type Single Correct Type 6g 7l C m

A truck moving 11 0 m s makes a head on inelastic collision with a stationary 1290 kg car After they move 8 75 m s What is the mass of the truck Unit kg Remember right is left is

Three balls are kept on a straight line on a smooth surface The first ball is projecte towards middle ball as shown It collides with middle ball of mass m which the collides with m3 We want m3 to move with maximum possible velocity after on collision What should be mass m in kg All collisions are head on and elastic m 4kg Vo m A m 9kg Am

A long plank of mass M rests upon a smooth horizontal surface A thin circular ring m R slips without rotation upon the plank The coefficient of friction between the wheel and plank is At t t s the ring s slipping ceases and pure rolling starts upon the plank 63 Find the value of t VM m 2M g 1 2m M m M m M 1 Vo puta Javo 0 0 V M 3 2 m M g art 64 Find the velocity of centre of wheel at t ts M a beage slugns 2 se 4 2 v M m M g 2v M m 2M g Vo 4 Vo m 2M m M do bigh sil ni sloining nove sopie 2m M YOA OM

Particle A of mass m moving with 1 velocity 31 1 ms collides with another particle B of mass m2 which is at rest initially Let v and be the velocities of particles A and B after collision respectively If m 2m2 and after collision V 1 31 ms the angle between Vand V is A 105 15 B C 45 D 60

A rectangular plate of dimensions 1 x b is in the X Y plane as shown in figure If the portion of this plate lying in the quadrant I is removed find the position of the centre of mass of the remaining part of the plate In which quadrant centre of mass of the remaining part lies Y b II III I IV X

another An object A of mass 1 kg is projected vertically upward with a speed of 20 m s At the same momen object B of mass 3 kg which is initially above the object A is dropped from a height h 20 m The two point like objects collide and stick to each other Find the kinetic energy of the combined mass just after the collision 2 kamoving

A uniform ring rolls on a horizontal surface without sliding The velocity of the centre is v It encounters a step of height 0 3 R where R is the radius of the ring Calculate the angular velocity of the ring just after the impact Assume that the ring does not return back and there is sufficient friction to avoid slipping Find the minimum value of v so that the ring ascends the step

and A of a rectangular plate ABCD each are placed at th in the figure A mass of 8 kg has to be the plate so that the centre of mass of should be at the centre O Then the r be placed at B 2kg F 4m H 0 2kg A G 1 1 m from O on OE 2 2 m from O on OF 3 2 m from O on OG

A particle of mass m moving east ward with a speed V collides with another particle of the same mass moving north ward with the same speed V The two particles coalesce on collision The new particle of mass 2m will move in the north east direction with a velocity A B 2 V due N E V 2 due N E 2 v due S E

Q 16 O 44 1 00 18 Consider the following statement When jumping from some height you should bend your knees as you come to rest instead of keeping your legs stiff Which of the following relations can be useful in explaining the statement O AP AP O FAI m4V AE A PE KE 0 E

Q 2 Two putty balls of equal mass moving with equal velocity in mutually perpendicular directions stick together after collision If the balls were initially moving with a velocity of 45 2ms each the velocity of their combined after collision is O45 2ms O 45ms 1 00 33 90ms

A rod of length L has a linear mass density Ax B A and B are constants Determine the location of the centre of mass from one end of the rod A B C D L 3A 2BL 3 2A BL L A 3BL 2 3A 2BL L 2AL 3B 3 AL 2B 2L AL 3B 5 AL 2B

Mass is distributed uniformly over a thin square plate If two end points of a diagonal are 0 0 and 2 2 what are the co ordinates of the center of mass of the plate O 2 1 O 1 1 O 1 0 0 1

A particle of mass 2 0 kg is moving in the xy plane at a constant speed of 0 80 m s in the x direction along the line y 4 m As the particle travels from x 3 m to x 3 m the magnitude of its angular momentum with respect to the origin is A not constant B 0 C 4 8 kg m s D 6 4 kg m s F 8 0 kg m s

plane which is circular at the ends with on a smooth radius r as shown in the figure The masses of the balls are m m m m 2 2 respectively What is 22 1 the minimum velocity which should be imparted to the first ball of mass m such that this nth ball will complete the vertical circle a n 1 n 1 3 mOO 5 gr 5 gr b n 1 4 3 2 d n 1 5 gr 5 gr

A particle of mass m moving with velocity u collides elastically head on with a particle of mass 2m at rest After collision the heavier particle moves with velocity 2u 3 2u

A hollow smooth U tube of mass 2m is lying at rest on a smooth horizontal surface Two small smooth balls of mass m moving with velocity u enter into the tube simultaneously Assuming all collisions to be elastic find out a final velocity of balls after long time b final velocity of tube after long time c minimum kinetic energy of the system during the process of collisions 2m

Two homogenous disc A and B of mass m and 3m having radii 3a a respectively are placed in touch The distance of centre of mass from centre of disc A is a 2a 3a 2 5a

5 A square plate and a circular plate made up of same meterial are placed touching each other on a horizontal table If the side length of square plate is equal to diameter of the circular plate then the centre of mass of the system will be 10 1 inside the square plate 2 inside the circular plate 3 at the point of contact 4 outside the system

Two balls are thrown simultaneously in air The acceleration of the centre of mass of the two balls while in air Is equal to g Is equal to g 2 Depends on the masses of two body Depends on the direction of motion of the ball

This means that the medians i e on the centroid Example 2 Three masses 3 4 and 5 kg are located at the corners of an equilateral triangle of side 1 m Locate the centre of mass of the system or the equilateral triangle lies in whe

Two small bodies of masses 1 kg and 4 kg are at rest on a smooth horizontal surface When they are at a separation of 10 m they are released to move under mutual attractive interaction Then which of the following statements is CORRECT A 1kg B 4kg They will never meet They will meet at a distance of 6 m from A To an observer at the centre of mass the particles have equal and opposite momenta They will meet at a distance of 8 m from B 10m

B of 2 Problem 7 19 A uniform piece of metal sheet is cut in the form as shown in the fig Locate the center of mass of the piece Sol y 30 20 10 0 10 20 30 30 20 10 0 3 12 10 20 30 X

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 a 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

116 Two particles of mass 5 kg and 10 kg respectively are attached to the two ends of a rigid rod of length 1 m with negligible mass The centre of mass of the system from the 5 kg particle is nearly at a distance of 1 2 3 4 50 cm 67 cm 80 cm 33 cm 122 A ray is incident at an angle of incidence surface of a small angle prism with angle A and emerges normally from the opposite If the refractive index of the material of th is u then the angle of incidence is near to 1 2A

4 0 kg 0 60 m Note Figure not drawn to scale 1 0 kg 0 10 m In order to model the motion of an extinct ape scientists measure its hand and arm bones From shoulder to wrist the arm bones are 0 60 m long and their mass is 4 0 kg From wrist to the tip of the fingers the hand bones are 0 10 m long and their mass is 1 0 kg In the model above each bone is assumed to have a uniform density 31 When the arm and hand hang straight down the distance from the shoulder to the center of mass of the arm hand system is most nearly A 0 25 m B 0 35 m C 0 37 m O 0 50 m e Purch

A thin uniform sheet of metal of uniform thickness is cut into the shape bounded by the line x a and y kx as shown Find the coordinates of the centre of mass A 2 0 4 2013 12 a 0 y kx y kx a C 5 X a D None of these

9 Two blocks of masses 10 kg and 30 kg are placed along a vertical line The first block is raised through a height of 7 cm By what distance should the second mass be moved to raise the centre of mass by 1 cm

D Consider a gravity free hall in which a tray of mass A carrying a cubical block of ice of mass m and edge L at rest in the middle figure 9 E4 If the ice melts b what distance does the centre of mass of the tray plu the ice system descend M m Gravity free hall

1 In a head on elastic collision of two bodies of equal masses a the velocities are interchanged b the speeds are interchanged c the momenta are interchanged d the faster body slows down and the slower body speeds up

A square plate of edge d and a circular disc of diameter d are placed touching each other at the midpoint of an edge of the plate as shown in figure 9 Q2 Locate the centre of mass of the combination assuming same mass per unit area for the two plates

3 Seven homogeneous bricks each of length L are arranged as shown in figure 9 E2 Each brick is displaced with respect to the one in contact by L 10 Find the x coordinate of the centre of mass relative to the origin shown Figure 9 E2 X

D A body moving towards a finite body at rest collides with it It is possible that a both the bodies come to rest b both the bodies move after collision c the moving body comes to rest and the stationary body starts moving d the stationary body remains stationary the moving body changes its velocity

16 A man of mass m is standing on a plank of equal mass m resting on a smooth horizontal surface The man starts moving on the plank with speed u relative to the plank The speed of the man relative to the ground is a 2u c zero m b d SIN SIT 2 4