Center of mass and momentum Questions and Answers

a small ball is attached to one end of a spring that has an unstrained length of 0 200 m the spring is held by the other end and the ball is whirled around in a horizontal circle at a speed of 3 00 m s the spring remains nearly parallel to the ground during the motion and is observed to stretch by 0 010 m by how much would the spring stretch by if it were attached to the ceiling and the ball allowed to hang straight down motionless

A solid sphere of uniform density has radius equal to R It has a cavity of radius R 2 such that the centre of mass lies on the surface of the cavity The distance between the center of sphere and centre of the cavity is A zero BR 14 c R 6 7R

8 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 NEET 2016 a m 60 60

3 A force F ai 3j 6k is acting at a poin r 21 6 12k The value of o for which about origin is CBSE AIPMT 201 d 1 angular momentum conserved a 1 is b 2 c zero

go round made of a ring like platform of radius R and mass M is revolving with angular speed w 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 c 3 N d 0 Rotate 11

A ladder of mass m and length stands against a frictionless wall with its feet on a frictionless floo If it is let go at an initial angle 8 60 then the angle at which the ladder loses contact with the wall is given as sin 1 N find N 60 0

At the top of the trajectory of a projectile direction of its velocity and acceleration are 1 perpendicular to each other 2 parallel to each other 3 inclined to each other at angle of 45 4 antiparallel to each other

cer 42 The particles attract each other and are permitted to towards each other along the line joining their mass At a particular moment of time their speeds an 2v What is the speed if their common centre of mas instant La Zero c v b 1 5v d 3v

Two billiard balls A and B each of mass 0 05 kg moving in opposite direction with a speed of 6 m s collide and rebound with the same 1 speed What is the total change in momentum of each ball A 0 6 kg m s 0 6 kg m s 1 0 6 kg m s 0 6 kg m s B 1 0 6 kg m s 0 6 kg m s 1 C D 1 0 3 kg m s 0 3 kg m s

A ball of mass 250 g moving with 20 m s strikes a vertical wall and rebounds along the same line with a velocity of 15 m s If the time of contact is 0 1 s the force exerted by the wall on the ball is A 87 5 N B 12 5 N C 12 5 N L 87 5 N

A block of mass m moving at a speed of u collides with another block of mass 2m at rest The lighter block comes to rest after the collision The coefficient of restitution is B 0 6 D 0 4 A 0 8 0 5

Point masses of 2 kg 3 kg 5 kg and 7 kg are placed at the corners of a square ABCD respectively whose each side is 1 m long The position of the centre of mass of the system is 14 A 12 B 17 15 C 17 m m 8 17 10 17 m m D 17 12 17 m m 10 21 10 1 17 8 17 m m

orm disc of mass m and radius R is pivoted at point P and is free to rotate in vertical plane The centre C of disc is initially in horizontal position with P as shown in figure If it is released from this position then its angular acceleration when the line PC is inclined to the horizontal at an angle 8 is JE P 00 2g cos emal 1 0 3R 2g sin 0 3 E 2 4 g sine 2R 2g sin e

c 8 9x 7 2 1 d 1 8 9 7 2 102 In a rectangle ABCD BC 2AB the moment of inertia along which axis will be A minimum a BC b BD c HF d EG ooks com H D Fig

The centre of mass of a system of two uniform spherical masses of 5 kg and 35 kg with centres of them 0 7 m apart is A 0 6125 m from 35 kg 0 6125 m from 5 kg B C D 0 35 m from 35 kg 0 35 m from 5 kg

stiffness k is attached at Q Find the frequency of sm of the disc if the string does not slide over the pulley Assume Io MI of the disc about O 24 The pulley shown in figure has a radius r moment of inertia I about its axis and mass m Find the time period of vertical oscillations of its centre of mass The spring constant of spring is k and the spring does not slip over the pulley 25 A long uniform rod of length L and mass M is free to rotate in horizontal plane about a vertical axis through its one end A spring of force constant k is connected horizontally uilibrium it is eeee 0 G

Two objects of same mass slide from the same height h from two smooth inclined planes with different angles Choose INCORRECT statement s A Impulse of their weight is same till they reach the bottom B Impulse of the resultant force is same till they are at half the initial height C Have same momentum when they reach at the bottom D Have same horizontal components of their momentum when they reach the bottom Your Answer BD Answer A B CD Solution Conceptual

Two blocks of mass 2kg and 3kg are connected with the massless spring of 200 N m If 2kg block is moving with a speed of 5 m s towards right and 3kg block is moving with a speed of 10 m s towards right when spring is in relaxed state then find the ratio of minimum speed of 2 kg block to that of 3kg block in subsequent motion 5m s 2kg oooooo 10m s 3kg smooth 15

Q4 A rocket is moving in a gravity free space with a constant acceleration of 2 ms along x direction see figure The length of a chamber inside the rocket is 4 m A ball is thrown from the left end of the chamber in x direction with a speed of 0 3 ms relative to the rocket At the same time another ball is thrown in x direction with a speed of 0 2 ms from its right end relative to the rocket The time in seconds when the two balls hit each other is 0 3 ms 0 2 s a 2 mas

A thin rod MN free to rotate in the vertical plane about the fixed end N is held horizontal When the end M is released the speed of this end when the rod makes an angle a with the horizontal will be proportional to see figure M 1 cos a 3 cosa 2 sin a 4 sin

A bomb initially at rest explodes by it self into three equal mass fragments The velocities of two fragments are 31 2 m s and 1 4 m s The velocity of the third fragment is in m s Question Type Single Correct Type 1 21 21 2 21 21 3 21 21

mass is whirled in a circular path constant angular velocity and its linear velocity is V e string is now halved keeping the angular momentum same the linear velocity is V B 2V C V D V 2

A neutron moving with velocity u collides elastically with an nucleus of mass number A If the collision is head on and the initial kinetic energy of neutron is E then the final 1 4 13 r of the neutron after collision is 1 A 1 3 A 1 A 1 E E 2 4 A 1 A 1 E E

6 A T shaped object with dimensions shown in the figure is lying on a smooth floor A force F is applied at the point P parallel to AB such that the object has only the translational motion without rotation Find the location of P with respect to C 2 I Lad SIW WIN 4 21 A Tu P 21 B

From a uniform circular plate of radius R and area A a small circular portion of area A 21 is cut out at a distance 3R 4 from the centre O as shown The centre of mass of leftover disc is at a distance x from 0 where x is

Q9 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 L 2 L b 3 d c 1 3 2L 3 201 4M 201 8M 20L 4M 201 6M

In the figure shown the mass of the disc as well as that of the trolley is M The spring is ideal and has stiffness k The trolley can move horizontally on the floor without friction and the disc can roll on the trolley surface without slipping The spring is compressed and the system released so that oscillations begin At the instant of release magnitude of mmmmmmm Acceleration of center of disc twice of that of trolley Acceleration of center of disc thrice of that of trolley Spring force is four times of friction Spring force is two times of friction

4 Two particles of masses m and 2m has initial velocity u 21 3j m s and u2 41 3 m s These particles have constant acceleration a 4 33 m s and 2 4 2 m s respectively Path of the centre of mass of this two particle system will be respectively A Straight line B Circular C Parabolic D Helical

the distance between a node and the next antinode is 1 7 5 2 15 3 22 5 4 30 16 A spherical shell and a solid cylinder of same radius rolls down an inclined plane The ratio of their accelerations will be 1 15 14 2 9 10 3 2 3 4 3 5 Five forces F1 F2 F3 F4 and Fs are acting on 17 with 4 964 1 HE y C

3 8H A solenoid wound over a rectangular frame If all the linear dimensions of the frame are increased by a factor 4 0 5 H 3 and the number of turns per unit length remains the same the self inductance increased by a factor of 1 3 3 27 2 9 4 63 71

When an external force is applied at the centre of mass of the system of an object then it undergoes Only translatory motion Only rotatory motion Both translatory and rotatory motion An oscillatory motion

A body thrown vertically up with velocity u reaches the maximum height h after T seconds Which of the following statement is correct At a height from the ground its velocity is 2 SIN At the time T its velocity is zero At the time 2T its velocity is u directed downward Both 2 and 3

Two particles of masses 1 kg and 2 kg are placed at a distance of 3m Moment of inertia of the particles about an axis passing through their centre of mass and perpendicualr to the line joining them is in kg m 1 6 2 9 3 8 4 12

A metal spherical shell of mass m is filled completely with nonviscous water of mass m 2 and is rolled down an inclined plane of height h The total kinetic energy of shell plus water and the velocity of the centre of the shell when it reaches the bottom of the plane is K and v respectively If water in the shell is freezed and then it is rolled down the corresponding values of kinetic energy and velocity are K and v respectively Then 0 K mgh O K mgh K v v

A wedge of mass 3m is kept on a smooth horizontal surface A block of mass m is released from top most point as shown Angle made by velocity of block with vertical downward with respect to ground when it just touches the ground 1 53 3 45 37 3m 2 60 4 30

Q18 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 Zu b NIE c zero d IE mmmm

9 Multiple Collisions in a Tube Inside a smooth circular tube of radius 5m a small ball A moves at speed 10 m s and strikes another ball B of double the mass located at diametrically opposite point as shown in figure If coefficient of restitution is 0 5 find the time when second collision occurs Lot If ball A starts at 0 it collides with Bat time t X 5 sec 10 As e 0 5 final speeds of balls A B are V m e zm by 3m U O ihs 3 vien 1 e m u 4 3m the internal between first second collision st divato ni onvol done ABE 0 Y Feupildo SS 2 4 S 2x sec 10 u a the at which second collision take place to t At 1 2x

D In a typical Indian Bugghi a luxury cart drawn by horses a wooden plate is fixed on the rear on which one person can sit A bugghi of mass 200 kg is moving at a speed of 10 km h As it overtakes a school boy walking at a speed of 4 km h the boy sits on the wooden plate If the mass of the boy is 25 kg what will be the new velocity of the bugghi

9 A man of mass M having a bag of mass m slips from the roof of a tall building of height H and starts falling vertically figure 9 E8 When at a height h from the ground he notices that the ground below him is pretty hard but there is a pond at a horizontal distance x from the line of fall In order to save himself he throws the bag horizontally with respect to himself in the direction opposite to the pond Calculate the minimum horizontal velocity imparted to the bag so that the man lands in the water If the man just succeeds to avoid the hard ground where will the bag land H h

A railroad car of mass M is at rest on frictionless rails when a man of mass m starts moving on the car towards the engine If the car recoils with a speed v backward on the rails with what velocity is the man approaching the engine

A bomb of mass 3m is kept inside a closed box of mass 3m and length 4L at its centre It explodes in two parts of mass m and 2m The two parts move in opposite directions and stick to the opposite sides of the walls of box The box is kept on a smooth horizontal surface What is the distance moved by the box during this time interval 10 Question Type Single Correct Type 2 L 00 16 4L

13 A particle of mass 3m at rest decays into two particles of masses m and 2m having non zero A velocities The ratio of the de Broglie wavelengths of the particles a 1 2 c 2 1 22 is b 4 d None of these 21 Di H va a c 22 V 1t la a

4 The balloon the light rope and the monkey shown i figure 9 E7 are at rest in the air If the monkey reaches the top of the rope by what distance does the balloon descend Mass of the balloon M mass of the monkey m and the length of the rope ascended by the monkey L M L Lo E

The elastic collision between two bodies A and B can be considered using the following model A and B are free to move along a common line without friction When their distance is greater than 1 m the interacting force is zero when their distance is less than d a constant repulsive force F N is present The mass of body A is mA 1 kg and it is initially at rest the mass of body B is m 3kg and it is approaching body A head on with a speed vo 2m s A B A The minimum distance between the two is 0 75m B Time taken to get minimum approach is 2sec C Velocity of m never becomes zero D Final velocity of ma is 3m s in leftwards

As shown in the figure below a rectangular block of mass M and length L is placed on a smooth table A small cube of mass m with negligible length is placed on the left end of the block with horizontal initial velocity v sliding to the right The coefficient of kinetic friction between the block and the cube is and the cube does not fall from the right end of the block What is the displacement in m of the rectangular block when the cube stops sliding on the rectangular block exactly at its right most end Take m 2 kg M 6 kg and L 10 m m

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 A B C 12 4 ow AC A 3 4 D MR 4 MR MR 4 10TT 16 MR R 4R X

FE9 7 A 100 ton tugboat is moving at 4 ft s with a slack towing cable attached to an 80 ton barge which is at rest Neglecting the resistance of the water determine the velocity of the tugboat after the cable becomes taut a 1 35 ft s b 2 22 ft s c 3 21 ft s d 4 68 ft s

Three long frictionless rods are fixed parallel to each other in a borizontal plane with separation d between adjacent rods The rods wear identical sleeves A B C and D each of mass m and charge q Initially the sleeves B C and D are arranged in a line perpendicular to the rods and the sleeve A is far away from them as shown in the figure In this way the sleeves B C and D are in a state of unstable equilibrium and have no electrostatic interaction with the sleeve A If the sleeve A is launched towards the right with an initial velocity u find velocities of all the sleeves when they acquire steady motion Consider all possible If u cases Here

42 The radius of gyration of a solid sphere of radi R about a certain axis is also equal to R If r is the distance between the axis and the centre of the sphere then r is equal to a R c 0 6R b d 0 5R 0 3R The block 4

2 c 336 k A bullet is fired normally towards an immovable wooden block It loses 25 of its kinetic energy in penetrating through a thickness x of the plank The total thickness penetrated by the bullet into the block is 2 Ar b 6 c 8x d 2x