Center of mass and momentum Questions and Answers

Three indentical bodies each mass M are at vertices of an equilateral triangle of a keeping the triangle as such by which angular the bodies should be rotated in their gravita fields so that the triangle moves along circumf of circular orbit 3GM 1 V L 3 GM V213 2 GM VI L 4 3 GM

5 For head on collision between two colliding balls of equal radii r the impact parameter is equal to 1 2r 3 More than 2r 2 Zero 4 Less than 2r

The moment of inertia of semicircular plate of radius R and mass M about axis AA in its plane passing through its centre as shown in the figure is 0 45 MR LA 0 A MR MR MR2

side 1 0 L L L From a uniform square plate of side L a square of L 12 is cut out from the centre and placed as shown Co ordinates of new centre of mass is 5L 3 y 3L 16 X 2 4 O 0 O 5L 16

A ball of mass m moving with speed u collides wit a smooth horizontal surface at angle 8 with it as shown in figure The magnitude of impulse imparted to surface by ball is Coefficient of restitution of collision is e using 0 1 mu 1 e cose 3 mu 1 e cose 0 Izmv My usino Vy eusin mullte STRUCT mu e sine mu e sine

A smooth hoop lies on a smooth horizontal table and is fixed A particle is projected on the table from a point A on the inner circumference of the hoop at angle 0 with radius vector If e be the coefficient of restitution and the particle returns to the point of projection after two successive impacts The final angle 0 made by velocity vector with radius of hoop is e 1 e tane e A tan0 C tane tane B tane e tane D tane tane e A

35 A tennis ball bounces down a flight of stairs striking each step in turn and rebounding to the height of the step above If the height of each step is d the coefficient of restitution is 1 1 du v 2 2

If the time interval between the first and the second impacts is T then 0 ev T gr 2

41 A R A thin uniform spherical sphell of radius R is cut such that upper portion of height upside down from same cross section Mass of sphere M Height of centre of mass from ground in final situation is B 47 50 R 5 1 R C 49 R 50 D R 5 is removed and put 39 50 R

A conducting rod of length is hinged at point 40 O It is free to rotate in vertical plane There exists a uniform magnetic field B in horizontal direction The rod is released from position shown in the figure When rod makes an angle from released position then potential difference between two ends of the rod is proportional to X 1 3 sin 0 O X X X 0 B l X X 2 l sin 0 4 sin 0 2

G balls of mass 20 g is firing 20 balls per second on the smooth horizontal table surface ABCD If the collision is perfectly elastic and balls are striking at the centre of table with a speed of 5 m s at an angle of 60 with the vertical just before collision then force exerted by one of the legs on ground is assume total weight of the table is 0 2 kg OSN Po h 1 N D Fig 1 223 U B P C r L

A block of mass m rests on a rough horizontal surface Coefficient of friction u When a bullet of mass m 2 strikes horizontally and get embedded in it the block moves a distance d before coming to rest The initial velocity of the bullet is k 2ugd then the value of k is m 2 a 2 m d H b 1 d 5

Two persons standing on a floating boat run in succession along its length with a speed 4 2 m s relative to the boat and dive off from the end The mass of each man is 80 kg and that of boat is 400 kg If the boat was initially at rest find the final velocity of the boat Neglect friction 1 0 6 m s 3 0 1 m s 2 0 7 m s 4 1 3 m s

2 If the ice at the poles melts and flows towards the equator how will it affect the duration of day night 3 When tall buildings are constructed on earth the duration of day night slightly increases Is this statement true or false

3 A disk A of radius r moving on perfectly smooth surface at a speed v undergoes an elastic collision with an identical stationary disk B Find the velocity of the disk B after collision if the impact parameter is d as shown in Figure A 1 v 1 vr d 4r d 2 1 vd 2r B 2

One solid sphere A and another hollow sphere B are of same mass and same outer radii Their moment of inertia about their diameters are respectively and I Such that B a 1 1 b 1 718 2004 c 1 1B d Tg dg their densitie

6 A particle of mass m is dropped on a fixed smooth inclined plane of angle 0 30 as shown in the diagram After collision particle moves horizontally Coefficient of restitution of collision is 1 e 1 3 e 1 C 30 2 e 4 e 11 11 2

A rod of length L is pivoted at one end and is rotated with a uniform angular velocity in a horizontal plane The value of x for point P where tension is of the tension at O 1 1 2 4 O x 0 P L4 X L

3 If linear density of a rod of length 4 m varies as 4 x then the position of the centre of gravity of the rod is 1 1 27 2 m E 10 3 m 2010 2 200 m 3 4 m

The moment of inertia about the axis 1 1 for system 23 of solid sphere shown will be M 5 kg R 1 m 1 O 1 48 kg m 3 70 kg m 1 2 60 kg m 4 50 kg m

A ring and a particle of masses 2m and m are kept as shown in the figure such that the CM of the combination lies at the origin Find x 2m R 0 m

Eight solid uniform cubes of edge I are stacked to gether to form a single cube with centre O One cube is removed from this system Distance of the centre of mass of remain ing 7 cubes from O is a c 7 31 16 31 14 b 31 16 d zero

Illustration 3 A dog of mass 10 kg boat so that it is 20 m from the shore It walks 8 m on the boat towards the shore and then stops The mass of the boat is 40 kg and friction between the boat and the water surface is negligible How far is the dog from the shore now 20 m Dog

of mass m is floating in air by a jet of out of a nozzle If the water strikes the ping pong ball with a speed v and just after collision water falls dead the rate of mass flow of water in the nozzle is equal to ong water emerging 1 3 2mg V mg M 2 mv g 4 None of these

in momentum F 1 3 of the following graphs the total change is zero 5 F 5 A 1 2 5 2 4 F LO 5 5 2 5 0 5

A bullet of mass m is fired from below into a bob of mass M of a long simple pendulum The bullet stays inside the bob and the bob rises to a height h The initial speed of the bullet will be 1 hg 3 M m m 2h m g M m 2 2h M m g m 4 2gh M m m

A disc of mass M and radius R is rolling without slipping with angular speed co on a horizontal plane as shown The magnitude of angular momentum of the disc about the origin O is 1 MR 0 2 MR 0 3 MR 4 2MR

Suppose a ball of mass m is thrown vertically upward with an initial speed v its speed decreases continuously till it becomes zero Thereafter the ball begins to fall downward and attains the speed v again before striking the ground It implies that the magnitudes of initial and final momenta of the ball are same Yet it is not an example of conservation of momentum Explain why

Mass of bigger disc having radius 2R is M A disc of radius R is cut from bigger disc Moment of inertia of disc about an axis passing through periphery and perpendicular to plane is 27 MR 29 MR 8 8 a b c 3 5 MR d 2MR

ision the system imm A body of mass 8kg at rest expolded into 3 pieces of masses 1kg 2kg and 5kg The first two pieces off perpendicular with velocities in the ratio 3 2 and 5 kg piece fly off at 10m s Then 1 2 1 Velocity of 1kg part is 30m s 3 Velocity of 1kg part is 15m s 2 Velocity of 2kg part is 20m s 4 Velocity of 2kg part is 10m s A ball strikes a smooth horizontal floor obliqualu

Six rods of the same mass m and length are arranged as shown in figure Calculate the coordinate of the centre of mass of the system y YA 1 3 276 l 4l 2 3 m m 2 4 zie l 5l 2 3 X

If momentum of an object is increased by 10 then its kinetic energy will increase by 1 20 2 21 4 19

A uniform rod of mass m and length L is suspended with two massless strings as shown in the figure If the rod is at rest in a horizontal position the ratio of tension in the two strings T T is 1 1 1 T 3L 4 2 1 2 T 2

11 A shell of mass 100 g moving with speed of 50 m s 3 1 along a straight line inclined at an angle tan to the horizontal bursts into two pieces The piece of mass 60 g starts moving horizontally with a speed of 50 m s The other piece moves with a speed of a 50 m s opposite to the first piece b 100 m s in vertically downward direction c 50 m s in the same direction as the first piece d zero remains at rest

45 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 a mV mV c b 2 mV mV d 3 m V 60 60 V

The wavelength of light in two liquids x and y is 3500 and 7000 then the critical angle will be 4 15 1 60 2 45 3 30

15 A block of mass 1 kg is moving along a line X Y 5 at a speed 2 2 m s If x and y are in meter then the angular momentum in kg m s of the mass about origin is 1 5 3 10 2 5 2 4 10 2

Man A of mass 60 kg pushes the other man B of mass 75 kg due to which man B starts moving with acceleration 3 m s The acceleration of man A at that instant is A 15 m s opposite direction C m s same direction A B 1 3 m s Smooth surface 15 2 15 D m s same direction B m s opposite direction

An object is projected with a speed 10 m s at an angle of 300 with the horizontal The object breaks down into n equal fragments during its motion One fragment is found to strike the ground at a distance of 3 m from the point of projection in the same azimuthal plane in which the object is projected If the centre of mass of the remaining fragments strikes the ground at distance of 7 3 m from the point of projection then the value of n is A 2 C 4 B 3 D 5 inclined to a vertical wall is P

24 A particle of mass m strikes a wall with speed w at an angle 30 with the wall elastically as shown in the figure The magnitude of impulse imparte to the ball by the wall is 1 mv V 30 30 2 mv

A thin non conducting horizontal disc of mass m having total charge q distributed uniformly over its surface can rotate freely about its own axis Initially when the disc is stationary a magnetic field B directed perpendicular to the plane is switched on at t 0 Find the angular velocity acquired by disc as a function of time if B kt where t is time B kt IR

A particle of mass m charge Q and kinetic energy T enters a transverse uniform magnetic field of induction B After 3 seconds the kinetic energy of the particle will be AT 3 3T 2 4 T 4 2T 73

A ball moving with a momentum of 15 kg ms 1 strikes against the wall at an angle of 30 and is reflected with the same momentum at the same angle Calculate impulse Chandigarh 08

same thickness The peripheries of the two dis system taking center of large disc at origin 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 y y kx y kx a

48 The period of revolution of planet A around the sun is 8 times that of B The distance of A from the sun is how many times greater than that of B from the sun 1 4 3 2 2 5 4 3

25m A skier plans to ski a smooth fixed hemisphere of radius R He starts from rest from a curved smoo R 14 surface of height The angle 0 at which he leaves the hemisphere is TR 4 I 0 R Z 0

A frog sits on the end of a long board of length L 10 cm The board rests on a frictionless horizontal table The frog wants to jump to the opposite end of the board What is minimum take off speed v in ms relative to the ground that the frog follows to do the trick Assume that the board and frog have equal masses UP CPMT 2015 1

Mass A hits B inelastically e 0 while moving horizontally with some velocity along the common line of centres of the three equal masses each of same mass Initially mass B and C are stationary and the spring is unstretched Then which is incorrect m A compression will be maximum when blocks have same velocity B velocity of C is maximum when A B is at rest C velocity of C is maximum when spring is undeformed D velocity of C is minimum when spring is undeformed B C k m wwwm Smc Corp Reg Office CG Tower A 46 52 IPIA Near City Mall Jhalawar Road Kota Ra resonance ac in E mail contact resonance ac in ADVCO

An insect of mass m is initially at rest at the one end of a stick of length L and mass M which rests on a smooth horizontal floor The coefficient of friction between the insect and stick is k Th insect starts moving to reach the other end in shortest possible time A The centre of mass of the plank has speed v kmg t w r t horizontal floor at time t M B Time taken by the insect to reach the other end is t 2LM k M m g C The magnitude of the linear momentum of the insect at time t is equal to kmgt D The maximum speed acquired by the stick is Vmax 2kLMm g M m m

If the collision of a ball of mass m is inelastic then the relation between 0 and o is where e is the coefficient of restitution Jous m 1 tana 3 tang tane cote 0La LE m 2 tana etane 4 A