Center of mass and momentum Questions and Answers

4 15 A 42 kg girl walks along a stationary uniform beam of mass 21 kg She walks with a speed of 0 75 m s What is the speed of the center of mass of the system of girl plus beam Ans 0 5m s

Read More Two masses M 1 kg and M 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 moved by centre of mass in first second after the start ism Find k Take g 10 ms 2 1 kg M M 2 kg

A sector cut from a uniform disk of radius 12 cm and a uniform rod of the same mass bent into shape of an arc arranged facing each other as shown in the figure If center of mass of the combination is at the origin what is the radius of the arc Your Answer

A bullet weighing 0 5 N and moving with a velocity of 400 m sec hits centrally a 30 N wood moving away at 15 m sec and gets embedded into it Find the velocity of bullet afte and K E lost

14 Two billiard balls A and B each of mass 50g and moving in opposite directions with speed of 5 m s each collide and rebound with the same speed If the collision lasts for 10 3 s which of the following statements are true a The impulse imparted to each ball is 0 25 kg ms and the force on each ball is 250 N b The impulse imparted to each ball is 0 25 kg ms and the force exerted on each ball is 25 x 10 5 N c The impulse imparted to each ball is 0 5 N s d The impulse and the force on each ball are equal in magnitude and opposite in directions

A Zener diode having breakdown voltage equal to 15V is used in a voltage regulator circuit shown in figure The current through the diode is o www 25092 1 5 MA Question Type Single Correct Type 2 10 MA 20V 3 15 MA 15V 1kQ

3 A uniform thin rod of length 2L is bent at right angles at a distance L from one end as shown in figure If length of rod is 1 8 m find the coordinate and position vector of the centre of mass of the system 2L

two particles of mass M1 and M2 and velocities U1 and U2 aU1 makes an elastic head on collision and the initial Kinetic energies of these two particles are equal and M1 comes to rest after collision then what is ratio of masses and velocities Two masses 2m and m are connected by an inextensible light string The string is passing over a light frictionless Pulley The mass 2m is resting on a surface and mass m is hanging in the air A particle of mass m strikes the mass m below from with velocity v0 and stick to it In another case a particle of mass m strikes the mass m with a velocity v0 from top and stick to it Calculate the ratio of velocities of mass m just after the collision in the first and second case

A block of mass 2kg is placed in front of spring with k 1 96x10 N m The spring is compressed 20 cm and then released from rest What is the maximum distance d will the block travel along the incline from lunching point to highest point if the surface is frictionless and the incline angle 0 30 0 300 Initial d 19 30 Final h

lock A of mass MA 1 kg is kept on a frictionless horizontal surface and attached by a light thread to another block B of mass MB 0 75 kg Block B is resting on the ground and thread and pulleys are massless and frictionless A sm nass m 0 25 kg moving with speed u 400 m s horizontally towards left sticks to the block A as shown in the figure Speed of block B in m s just after collision between the block A and bullet is x Then the value of x is u 400m s A Rm 3 4 kg

Two bodies travelling along the same line with a relative velocity of 2 m s undergo one dimensional elastic collision After collision their directions of motion remain unchanged During collision the graph of the force exerted by one body on the other versus time is as shown Find the value of F kN in the graph if the harmonic mean of the masses of the two bodies is 5 kg force kN time ms

QA uniform rod of mass m and length is fixed at one end released from horizontal position as shown in the figure The angular velocity of the rod when the rod makes an angle 60 with vertical is Hinged m 1 A B C D 3g 21 4g 31 2g 3g 7

Three particles of equal masses are placed at the corners of an equilateral triangle as shown in the figure Now particle A starts with a velocity v towards line AB particle B starts with a velocity V towards line BC and particle C starts with velocity v3 towards line CA The displacement of centre of mass of three particle A B and C after time t will be given if v V2 V3 A zero V V V3 3 V 3 3 V V V3 V3 B VII 2 3 C

1 A small ball of mass m suspended from the ceiling at a point O by a thread of length moves along a horizontal circle with a constant angular velocity w Choose from following the correct option s Option D A B C Angular momentum is constant about O Angular momentum is constant about C Vertical component of angular momentum about O is constant Magnitude of angular momentum about O is constant Rate this questio

The vector position of a 3 40 g particle moving in the xy plane varies in time according to r 31 3 t 2 t where t is in seconds and r is in centimeters At the same time the vector position of a 5 85 g particle varies as r 31 2 t 6 t a Determine the vector position in cm of the center of mass of the system at t 3 00 s cm b Determine the linear momentum in g cm s of the system at t 3 00 s g cm s P cm c Determine the velocity in cm s of the center of mass at t 3 00 s cm cm s d Determine the acceleration in cm s2 of the center of mass at t 3 00 s cm s e Determine the net force in N exerted on the two particle system at t 3 00 s

A ring of radius r is spun about a vertical axis with an angular velocity w in a horizontal plane A uniform magnetic field of magnitude B exist in the region in vertical direction The emf induced in the ring is Tu Bw Bro Zero

R A uniform of mass M 1kg radius 1m is moving towards right with velocity vs 20m s and having angular velocity wo 4rad s about the axis perpendicular to plane of the disc passing through centre of disc Suddenly top point of the disc gets hinged about a fixed smooth axis The angular velocity in rad s of disk about new rotation axis is

PHYSICS CHEMISTRY Question No 21 Single Co Co ordinates of centre of m 712 BIO 1 2 2 3 1 3 22 121 3 3 2kg H 1m 4kg 1m 1m 2kg 11 16 6 21 26 31 36 41 2 7 2 22 12 17 7 37 42 22 HEMISTRY Attempted Review 4 N 13 18 A 43

When an ideal diatomic gas y 1 4 is heated at constant pressure what is the fraction approximate of the heat energy supplied which increases the internal energy of the gas Question Type Single Correct Type 1 0 2 2 0 3 3 0 5 4 0 7

Two identical blocks each of mass 1 kg are join together with a compressed spring The system at any time after releasing is moving with unequal speed in the opposite direction as shown in figure Choose the incorrect statement 3ms Option A B C D mmmmmm 5ms it is not possible whatever may be the speed of the blocks the centre of mass will remain stationary the centre of mass of the system is moving with a velocity of 2 m s 1 Rate this question the centre of mass of the system is moving with a velocity of 1 m s 1

Two blocks connected to the spring are given velocities as shown in figure Spring is at natural length position What is the potential energy of spring in SI units when kinetic energy of the system is minimum 1m s 5kg moooooo mmmmm 10kg 2m s

A thin metal plate is being bombarded by a perpendicular beam of gas particles from both sides The mass of these particles is m their veloc ity before striking is v and there are n particles vol in each beam Each beam has an area A and the collisions are elastic What force in N is needed to move the plate with a constant velocity u Take m n 10 per m A 1m v 10 m s u 2m s 10 27 kg LI

Graphs a and b show the effect of carts A and B colliding separately with a standard cart S List the three carts in order of increasing mass m m ms MA ms MB m m m Om m ms VA A a S b B t

A thin uniform stick of length and mass m is held horizontally with its end B hinged on the edge of a table Point A is suddenly released The acceleration of the centre of mass of the stick at the time of release is AIPMT Mains 2007 3 A 49 3 B 79 2 C 7 D 17 5 B

3 With reference to figure of a cube of edge a and mass m which of lo the following is the incorrect statement O is the centre of the cube a The moment of inertia of cube ma about z is I I I c Ix ly D A H E Of C B F y 2 b The moment of inertia of cube about z is I ma 2

26 A ball strikes a horizontal floor at an angle 0 45 The coefficient of restitution between 1 the ball and the floor is e 2 of its kinetic energy lost in collision is 3 1 5 2 3 3 311 4 The fraction 4 1 14 26

All sides of an equilateral triangle are diameter of three identical uniform semicircular rings each of mass m Plane of each ring is perpendicular to the plane of paper Then moment of inertia of this system of three semicircular rings about an axis through centroid of triangle and perpendicular to plane of paper is 0 5ma 24 5ma 16 5ma 8 5ma V av

A projectile moving with 20 m s in horizontal direction explodes into two equal pieces One piece moves vertically down at 30 m s The speed and direction of motion of second piece is 1 5 m s 53 2 50 m s 37 4 10 m s 45 3 10 m s 53 Two blocks A and B of masses 1 kg and 2 kg are connected together by a spring and are resting on 1 2 30 F 3 Ta

If a cylindrical container filled with mercury is rotated with an angular velocity about its vertical axis of symmetry the mercury air interface takes shape of a paraboloid of revolution If this surface is used as a mirror where should a photo film be placed to get a clear picture of a distant star Acceleration of free fall is g 9 200 alsove lowest point of

A stationary object explodes into two fragments of masses m and 2m respectively If the energy of explosion is E the KE of the centre of mass of the system is 1 E 2 2E 55 Y 199RICE 3 0 4 15 lo f bo

Consider a rectangular plate of dimensions a x b If the plate is considered to be made up of four a b rectangles of dimensions 22 one out of the four rectangles find the position where the centre of mass of the remaining system will be b y 0 0 and we now remove

13 Two point masses m and m at rest in gravity space are released from distance d Find the velocity of the CM of the system at the time of collision of particles 1 Zero 2 2 3 3 4 None

c 8 75 d 8 751 3 A body of mass 4 kg is moving with momentum of 8 kg m s A force of 0 2 N acts on it in the direction of motion of the body for 10 s The increase in kinetic energy is 10 a 101 b 8 5 c 4 51 d 4

TEACHER PRACTICE ANOTH A billiard ball moving at 5 40 m s strikes a stationary ball of the same mass After the collision the first ball moves at 4 48 m s at an angle of 34 0 with respect to the original line on motion Assuming an elastic collision and ignoring friction and rotational motion find the struck ball s velocity after the collision magnitude m s direction with respect to the original line of motion

A block of mass 15kg is kept at rest on a frictionless surface Another mass 5kg moving at a speed of 9m s collides with mass 15kg After the collision the 5kg block comes to rest Determine the coefficient of restitution m 15 kg m 5 kg A B C 3 1 2 1 u 9m s u 0

4 All of these 166 A thin uniform rod has moment of inertia about an axi parallel to its length at a certain distance If on heating its length increases by 2 then moment of inertia of ro will change by 1 0 2 1 4 4

CONSERVATION OF MOMENTUM 42 Which one of the following statements is not true a The same force for the same time causes the same change in momentum for different bodies b The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction in which the force acts c A greater opposing force is needed to stop a heavy body than a light body in the same time if they are moving with the same speed d The greater the change in the momentum in a given time the lesser is the force that needs to be applied he

39 A ball of mass m strikes a rigid wall with speed u at an angle of 30 and get reflected with the same speed and at the same angle as shown in the figure If the ball is in contact with the wall for time t then the force acting on the wall is musin 30 a 1 mucos 30 b 2mu sin 30 t 2mucos 30

Q21 Two blocks M and M having equal mass are free to move on a horizontal frictionless surface M is attached to a massless spring as shown in figure Initially M is at rest and A is moving toward M with speed v and collides head on with M a While spring is fully compressed all the KE of Myis stored as PE of spring b While spring is fully compressed the system momentum is not conserved though final momentum is equal to initial momentum c If spring is massless the final state of the M is state of rest d If the surface on which blocks are moving has friction then collision cannot be elastic M m M m V rw

A uniform disc of diameter R is put over another uniform disc of radiu of same thickness and density The peripheries of these two discs tou each other The centre of mass of the system from centre of big disc Smaller disc O Bigger disc O O O R 10 3R 5

lens and the object position u as shown in the figure The focal length of the lens used was 2 b ca A bullet of mass M hits a block of mass M The transfer of energy is maximum when 1 M M 2 M 2M 3 M M 4 M M

The wavelength of the light received from a galaxy is 0 4 greater than the wave length on the earth then the velocity of galaxy relative to the earth will be 1 1 2 107 m sec 3 1 2 105 m sec 2 1 2 106 m sec 4 1 2 x 10 m sec

169 2 The mass of a hydrogen molecule is 3 32 10 27 kg If 1023 hydrogen molecules strike per second a fixed wall of area 2 cm at an angle of 45 to the normal and rebound elastically with a speed of 10 m s then the pressure on the wall is nearly 1 2 35 x 10 N m 3 2 35 x 10 N m 2 4 70 x 10 N m 4 4 70 x 10 N m

42 180 A disc of mass m and radius R is rolling without slipping as shown in the figure The velocity of the point P will be RIN P 0

A uniform rigid square loop of mass m side 1 is free to rotate about an axis in xy plane passing through one corner as shown A constant current I is flowing in loop In space magnetic field B 1 is present Initially loop is held at rest in xy plane On releasing It s instantaneous angular acceleration will be space is gravity free A 3 2 21 2 18 B 15 B D

During a figure skating competition an ice skater is rotating at 2 0 rad s When the ice skater draws her arms and legs close to her torso her moment of inertia decreases from 1 5 kg m to 0 30 kg m Determine her final angular velocity in radians per second

A rotating table completes one rotation in 10 sec and its moment of inertia is 100 kg m A person of 50 kg mass stands at the centre of the rotating table If the person moves 2m from the centre the angular velocity of the rotating table in rad sec will be 1 2 30 2 20 30 3 2 3 4 2

d 31 5j 3k diametric axis is 25 kg loment of inertia of a disc of radius R about a a parallel axis at a distance R 2 from the centre is m 2 The MI of the disc about MPPMT 2013 a 31 25 kg m e 50 kg m Jugi b 37 5 kg m d 62 5 kg m Mm

Q 33 Two metal spheres suspended by vertical cords initially just touch as shown in Fig Sphere 1 with mass m 30g is pulled to the left to height h 8 0 cm and then released from rest After swinging down it under goes an elastic collision with sphere 2 whose mass m 75 g What is the velocity v of sphere 1 just after the collision a 34 cm s b 54 cm s c 74 cm s d 94 cm s Ans B AD 1 2 m m Fyn

Q 9 A pan of mass m 1 5 kg and a block of mass M 3 kg are connected with each other by a flexible light and inextensible string passing over a small light and frictionless pulley Initially the block is resting over a horizontal floor as shown in Figure At t 0 an inelastic ball of mass mo 0 5 kg collides with the pan with velocity Vo 16 m s vertically downwards Calculate the maximum height upto which the block rises M a 16 cm b 32 cm c 64 cm d 96 cm MB