Center of mass and momentum Questions and Answers

A ball of mass m collides elastically with an identical ball at rest with some impact parameter 100 energy transfer can never take place 100 energy transfer may take place angle of divergence between the two balls must be 90 angle of divergence between the two balls depend on impact parameter

A tennis ball with small mass m sits on the top of a basketball with large mass m The bottom of the basketball is at a height h above the ground and the bottom of the tennis ball is at a height h d above the ground The balls are dropped from rest Here all collisions are elastic and m m The height from the point of collision up to which the tennis ball bounce is

A 10 0 kg object with an initial velocity of 8 0 m s to the east collides with a stationary 4 0 kg cookie tin Just after the collision the object has a velocity of 4 0 m s at an angle of 37 north of east Just then what is the velocity of the cookie tin O A 121 61 OB 121 7 O c 8i 13j OR 51 97

A ball A moving with certain velocity in positive x axis collides with a stationary ball B After collision their directions of motion make angles a and 3 with the x axis The possible values of a and Bare OA a 30 and 45 Ba 90 and B 120 Oc a 0 and B 30 D a 45 and B 0

A 4 0 kg particle like object is located at x 0 y 2 0 m a 3 0 kg particle like object is located at x 3 0 m y 1 0 m At what a x and b y coordinates must a 2 0 kg particle like object be placed for the center of mass of the three particle system to be located at the origin OA 5 5m 4 5m OB 3 5 m 4 5m OC 4 5m 5 5m OD 4 5 m 3 5m

A cricket ball of mass m hits another stationary ball of the same mass The coefficient of restitution for the above collision is 0 6 The ratio of the velocities of the two balls after collision will be A 1 4 B 1 2 c 1 1

A large open tank has two small holes in its vertical wall as shown in figure 7 72 One is a square hole of side L at a depth 4y from the top and the other is a circular hole of radius R at a depth y from the top When the tank is completely filled with water the quantities of water flowing out per second from both holes are the same Then R is equal to L A 2 A 2 L T 4y 2R Figure 7 72 EES D 2 Sill 111 B 2TL L 2

A rocket of mass 800 kg is launched from a gravity free space If rate of fuel consumption is 300 kg min and velocity of exhaust gases is 20 m s then the acceleration of rocket after 1 minute will be Question Type Single Correct Type 1 0 125 m s 27 55 m s 3 5 m s

n which of the following graphs the total change in momentum is zero x F 5 b LL F 50 b 2

A spacecraft can gain in mechanical energy as they encounter a planet This may appear as a violation of the conservation of energy but it is not The gained energy is at the expense of the orbital energy of the plang The easiest way to see how this works in principle is to treat the problem as an one dimensional collision Let the spacecraft have mass m and just before the encounter a velocity v the planet of mass M and velocity V Both velocities are relative to the sun and they are in opposite directions Thus the angle between v V is 180 Assume that the space craft round the planet and depart in opposite direction Thus after the encounter the velocity of the space crafts is in the same direction as of V Assume M m 41 What is the speed of spacecraft after the encounter in terms of m M and speed of the spacecraft before the encounters and the speed of the planet before the encounter M m A B V 2v M m C 4M m M m V 2MV M m V 2VM M m Mm M m D None of these

A steel wire of length 2 0 m is stretched through 20 mm The cross sectional area of wire is 40 mm Calculate the elastic potential energy stored in the wire in stretched condition Young s modulus of steel 2 0 10 N m

The options are 1 24 kgm 2 2 12kgm 2 3 30kgm 2 36kgm 2 11 A ring has mass of 6 kg and radius of 2 What is moment of inertia of this ring abc a tangent to the circle of ring in its plan NCERT Pq 16

8 A liquid of density p is coming out of a hose pipe of radius a with horizontal speed v and hits a mesh 50 of the liquid passes through the mesh unaffected 25 looses all of its momentum and 25 comes back with the same speed The resultant pressure on the mesh will be a pv 3 c pv b P 4 d p JEE Main

11 15 The centre of mass of triangle shown in figure has co ordinates h 2 b 2 y y b 2 h 2 X

Q No 36 A quarter sector of a uniform disc of radius R is shown in figure The coordinates of center of mass is 1 2 3 3 Cornet bopper 2 2R 2R 3 3 2R 4R 3m 3m 4R 4R 3m 3m 4R 2R 3m 3m R R

Two fishermen fish in the lake are sitting in a motionless boat The fishermen exchange places Mass of the boat is 280 kg mass of one fisherman is 70 kg weight of the second is 140 kg distance between fishermen is 5 m Resistance of water can be neglected The displacement of the boat is 0 71 m The displacement of the lighter fisherman is same in magnitude to the displacement of the heavier fisherman The displacement of heavier fisherman is lesser in magnitude to the displacement of lighter fisherman The displacement of boat is in the same direction as that of the lighter fisherman

A yo yo shaped device mounted on a horizontal frictionless axis is used to lift a 30kg box as shown in figure The outer radius R of the device is 0 50 m and the radius r of the hub is 0 20m When a constant horizontal force of magnitude 152 N is applied in the left direction to a rope wrapped around the outside of the device the box which is suspended from a rope wrapped around the hub has an upward acceleration of magnitude 0 80 m s What is the rotational inertia I in kg m of the device about its axis of rotation

A circular plate has a uniform thickness and has a diameter 56cm A circular dis c of diameter 56cm A circular disc of di ameter 42 cm is removed frome one ed ge of the plate the distance of centre of mass of the remaining portion from the centre of the circular plate is

A 1 kg ball moving at 12 m sec collides head on with 2 kg ball moving in the opposite direction at 24 m s If the coefficient of restitution is 2 3 then how much energy is lost in collision 1 240 Joule 2 120 Joule 3 360 Joule

17 In the equation S a bt ct S is measured in metres and t in seconds The unit of c is A Metre B Second C Metre second D Metre second 18 N different particles are all situated at a distance R from the origin The distance d of the centre o mass of the particles from the origin is A d R B dz R C d R D d R

The linear mass density of a thin rod of length varies with the distance x from one end as A A The position of centre of mass of rod from same end is at a distance of sys 3 3l 4 2 2 l 4 4

A thin circular disc of radius R is cut into two halves One half of the disc has mass m and is shown below The moment of inertia of the half disc about AB is 1 1 mR 2 Catalyst m A B MR

A hemisphere and a solid cone of same density have a common base The centre of mass of the common structure coincides with the centre of the common base If R is the radius of hemisphere and h is height of the cone then h A 2 2 3 R B h 1 R 3 C 3 R D h R 1 3

15 Four ic length 1 form a square frame Moment of inertia of this frame about an axis through the centre of the square and perpendicular to it plane is Show with diagram diagram 4 a M 3 13 M1 3 c 2 b M d M 3 which of the

An infinite number of bricks are placed one over the other as shown in the figure Each succeeding brick having half the length and breadth of its preceding brick and the mass of each succeeding bricks being 1 4th of the preceding one take O as the origin the x coordinate of centre of mass of the system of bricks is a 3a B M b 2 C M 4 a 2 3a O D 2a

A person holding a rifle mass of person and rifle together is 100 kg stands on a smooth surface and fires 10 shots horizontally in 5 s Each bullet has a mass of 10 g with a muzzle velocity of 800 m s The final velocity acquired by the person and the average force exerted on the person are a 0 08 m s 16 N b 0 8 m s 8 N c 1 6 m s 16 N d 1 6 ms 8 N

A shell of mass 5m acted upon by no external force and initially at rest bursts into three fragments of masses m 2m and 2m respectively The first two fragments move in opposite directions with velocities of magnitude 2v and v respectively The third fragment will 1 Move with a velocity v in a direction perpendicular to the other two 2 Move with a velocity 2v in the direction of velocity of the first fragment 3 Move with a velocity v in the direction of velocity of the second fragment A Ro at rest

A larger ring of mass M and two small rings of mass m start rotating with angular velocity wo from the position as shown in figure Initially small rings are close to axis There is no friction at any contact surface Then as time passes Consider the motion of small rings till they move upto the bottom most point www Question Type Single Correct Type 1 2 100 3 Angular momentum of system increases Angular momentum of system decreases Angular momentum of small rings increases continuously Angular momentum of small rings first increases and then decreases

A disc of radius R is cut out from a disc of radius R2 as shown in figure If the disc left has mass M then find moment of inertia of the disc left about an axis passing through its centre and perpendicular to its plane R R

Two balls of masses m and m are separated from each other by a powder charge placed between them The whole system is at rest on the ground Suddenly the powder charge explodes and masses are pushed apart The mass m1 travels a distances and stops If the coefficients of friction between the balls and ground are same the mass m stops after travelling the distance 1 2 CA II m m m S 2 S A S m m m

44 An impulse J is applied on a ring of mass m along a line passing through its centre O The ring is placed on a rough horizontal surface The linear velocity of centre of ring once it starts rolling without slipping is a J m J b J 2m O c J 4m TT d J 3m

29 A uniform rod AB of mass m and length 1 is at rest on a smooth horizontal surface An impulse J is applied to the end B perpendicular to the rod in horizontal direction Speed of particle P at a distance from the centre towards A of the rod after time 1 6 t ml 12J a 2 m is b J 2m c d 2 m

13 Three solid point like masses each of m 2 kg are connected by massless rods 50 cm long in a plane shown What is the moment of inertia I of the device about an axis perpendicular to the plane A about P 1 5 kg m C about C 6 kg m Ans A B 120 B 50cm 120 B about A 3 kg m D about B 4 5 kg m

3 A souvenir is constructed by 3 light rods light strings and four objects as shown If the system is in equilibrium what is mass m3 in gm m Ans 84 00 Sol m 9 gm m 42 gm m 84 gm 4cm 3cm 2cm 4cm 3cm 4cm 12gm m m

40 Pts Four communication satellites are placed in geostationary orbits at longitudes with corresponding masses in parentheses 20 4500 kg 110 5200 kg 170 4700 kg and 300 6000 kg How far from the center of Earth is the center of mass of these four spacecraft How far from the North Pole is the center of mass Write numerically the vector from the North Pole to the center of mass

small disc of mass M and radius R 3 3 21 ar disc of radius R and mass 9M concentrically The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its centre is 1 MR2 2 4MR 4 MR is removed a 40 MF 9 MR

A crate of mass m is dropped vertically onto a conveyor belt that is moving at v m s A motor maintains the belt s constant speed The belt initially slides under the crate After a short time the crate is moving at the speed of the belt During the period in which the crate is being accelerated find the work done by the motor which drives the belt A mv B mv 3 mv 3 D mv

3 a 4 2 a A thin uniform flat plate is in shape of L as shown The mass of lamina is 6 kg The position of centre of mass from point O NCERT Pg 147 0 2 O y 0 0 1 2 1 1 2 1 Plate X 2 0 6 1 97 13j 11k 3 9i 7j 11k The force acting i 2 3k N Find about origin if positi 71 31 5k m 1 i 16 11k 3 i 16 11k

Two balls of equal mass of 4 kg each are moving with velocity 4 m s towards each other collides inelastically If the coefficient of restitution is 0 5 then the loss in kinetic energ due to collision will be 64 J 16 J 24 J 48 J

3 8 m 4 1 m 4 An elevator can carry a maximum load of 900 kg elevator passengers is moving up with constant speed of 2 m s 1 A constant frictional force of 5000 N opposes the motion What minimum power is delivered by motor in HP NCERT Pg 128 X37 5 HP 3 42 5 HP 2 32 5 HP 4 50 2 HP 17 In ar 104 nucl resu frac 0 1

A rope with mass M 2 3 kg and length L 10 m is held in the position shown with one end attached to support Assume that only a negligible length of the rope hangs below the support The rope is released at t 0 Find the force in newton that the support applies to the rope at t 1 sec Take g 10 m s

A thermometer of mass m is filled with mercury of mass V m and placed in a gravity free space without touching anything As temperature rises mercury expands and ascend in thermometer If height ascend by mercury in thermometer is h then by what height COM of mercury thermometer system descend Zero min m m h m m m m2 h E Q

Attempt All 35 questions Find wrong statement 1 Radius of gyration depends on mass of the object as well as distribution of mass 11 Radius of gyration depends only on mass of the object III Radius of gyration depends only on distribution of mass IV Radius of gyration depends on angular velocity of the object 1 11 1 I II III IV V

1 A circular disk of moment of inertia I is rotating in a horizontal plane about its symmetry axis with a constant angular speed co Another disk of moment of inertia I is dropped coaxially onto the rotating disk Initially the second disk has zero angular speed Eventually both the disks rotate with a constant angular speed of The energy lost by the initially rotating disc to friction is 1 lok 1 2 4 lb 00 1 12 3 2 1 1 2 11 b 2 1 1b 16 4 4 1 x 00 00

A man of mass M stands at one end of a plank of length L which lies at rest on a frictionless horizontal surface The man walks to the other end of the plank If the mass of the plank is M 3 the distance that the man moves relative to ground is B MI A L C 3L 4 D 1 4L 3

10 The force acting on a body moving along x axis varies with the position of the particle as shown in the figure The body is in stable equilibrium at 1 99 1 x x 2 x x 3 both x and x 4 neither x nor X X X runs at a spee

A block of mass 0 9 kg attached to a spring of force constant k is lying on a frictionless floor The spring is compressed to 2 cm and the block is at a distance 1 2 cm from the wall as shown in the figure When the block is released it makes elastic collision with the wall and its period of motion is 0 2 sec Find the approximate value of k k brrroos 1 2 cm

A thin wire is bent in form of a helix of radius R and height H The pitch of helix is H 2 and mass pe unit length of wire is Moment of inertia of wire about the axis of helix is A B C D HR 2 R H 16 R AR H 16 R None of these

Block A in the figure has mass 1 00 kg and block B has mass 3 00 kg The blocks are forced together compressing a spring S between them then the system is released from rest on a level frictionless surface The spring which has negligible mass is not fastened to either block and drops to the surface after it has expanded Block B acquires a speed of 1 20 m s https session masteringphysics com myct assignmentPrint View assignmentID 9234532 6 18 2021 Part A What is the final speed of block A ANSWER Correct HW Ch08 Part B How much potential energy was stored in the compressed spring mA 1 00 kg S mB 3 00 kg 2 6

A point object is at 30 cm from a conve lens 3 2 of focal length 20 cm The fin image of object will be at infinity if 1 another concave lens of focal length 60 c is placed in contact with the previous lens 2 another convex lens of focal length 60 cm placed at a distance of 30 cm from the first ler 3 the whole system is immersed in a liqu of refractive index 4 3 4 the whole system is immersed in a liquid