Center of mass and momentum Questions and Answers

Calculate the strength of the magnetic field at a distance of 20 cm from a pole of strength 40 Am in air Find the induction at the same point

2 A person taking in his hands spheres each of mass 2 kg is standing on a table revolving with an angular velocity of 10 rad s His arms are extended and each sphere is at a distance of 1 m from the axis of rotation If the moment of inertia of the person and the table about the axis of rotation be 1 kg m then what will be the kinetic energy of rotation of the whole system If the person pulls in his arms so that each sphere is now at a distance of 0 3 m from the axis of rotation then what would be the new kinetic energy Explain this difference

5 A cubical block of side a is moving with velocity v on a horizontal smooth plane as shown it hits a small ridge at point O The angular speed of the block after it hits O is 1 3 3v 4a 3v 120 a M 2 3v 2a 4 Zero

A rod of length L is placed along the x axis between x 0 and x L The linear density mass length of the rod varies with the distance x from the origin as Rx Here R is a positive constant Find the position of centre of mass of this rod

In a vertical plane inside a smooth hollow thin tube a block of same mass as that of tube is released as shown in figure When it is slightly disturbed it moves towards right By the time 5 the block reaches the right end of the tube then the displacement of the tube will be where R is mean radius of tube Assume that the tube remains in vertical plane 1 2R TU R 2 2 4R TC 4 R part Take g 10 m 1 25 m 3 15 m A hemisphere of free to slide wi horizontal table placed on the particle is di velocity then the particle re hemisphere a when velocity 1 4v

the false statement 1 In elastic collision KE is not conserved during the collision 2 The coefficient of restitution for a collision between two steel balls lies between 0 and 1 3 The momentum of a ball colliding elastically with the floor is conserved 4 In an oblique elastic collision between two identical bodies with one of them at rest initially the final velocities are perpendicular

32 In the arrangement shown the pendulum on the to collide with other pendulum which is at rest A left is pulled aside It is then released and allowed perfectly inelastic collision occurs and the system rises to a height h 4 The ratio of the masses m m of the pendulum is 1 a 1 c 3 m ht 1 1 m b 2 d 4

Find moment of inertia of a uniform annular disc of mass 100 g having inner radius 10 cm and outer radius 20 cm about an axis passing through its centre and perpendicular to its plane 1 2 5 x10 kg m 3 5 x 10 kg m 2 1 5 x 10 3 kg m 4 6 10 kg m

Two bodies of same mass tied with an inelastic string of length lie together One of them is projected vertically upwards with velocity 6ge Find the maximum height up to which the centre of mass of system of the two masses rises

Two particles m 1 2 kg and m 3 kg have position m2 vectors 1 ti 2t2j 2 tk where r2 i 2t j 5k position vectors are in metres and time in seconds Find i position vector of centre of mass ii velocity of centre of mass and iii acceleration of centre of mass i 2t 3 i 4t 6t j 4t 15 k ii 2i 8t 18t j 4k iii 8 36t j 5

B 32 J C zero D can t be obtained A body of mass 2 kg is kept on a rough horizontal surface as shown in the figure Find the work done by frictional force in the time interval t 0 tot 5 sec 10 N 2 kg 30 0 5 10 N

Mass of the pulley is m radius is R Assume pulley to be disc Block of mass m is released from the position shown String is massless inextensible There is no slipping between rope and pulley The impulse exerted by the string on the pulley at the moment string becomes taut is J is equal to 2m gR J VM v m M Mrm 3 wwwwwwww m R m R V 16 L

ET A metre stick is placed vertically at the origin on a frictionless surface A gentle push in x direction is given to the top most point of the rod when it has fallen completely of centre of rod is at b 0 5 m x coordinate a origin d 0 5 m c 1m om and mand velocities v and

A railway flat car has an artillery gun installed on it The combined system has a mass M and moves with a velocity vo The barrel of the gun makes an angle a with the horizontal A shell of mass m leaves the barrel at a speed u relative to barrel in the forward direction The speed of the flat car so that it may stop after the firing is 1 mu M m mu 005 O 2 Mu M m co COS a 4 M m u cos a 4 M 1 ML m 3 L A particle of of 45 with 20 2 m s the particle a result of

5 The x y coordinates of the centre of mass of a uniform L shaped lamina of mass 3 kg is a 516 5 m m 6 c m b 1 m 1m 6 F 6 m m 5 5 d 2 m 2 m 2 m K2 m

Three identical balls ball I ball II and ball III are placed on a smooth floor on a straight line at the separation of 10 m between balls as shown in figure Initially balls are stationary Ball I is given velocity of 10 m s towards ball II collision between ball I and II is inelastic with coefficient of restitution 0 5 but collision between ball II and III is perfectly elastic What is the time interval between two consecutive collisions between ball I and II II 10 m III e

A circle and a square wire frame each of mass m are arranged as shown in the diagram The diameter of the circle and the edge of the square are 2R each Find moment of inertia of this configuration about XX 2R 17mR A B D 6 11mR 6 19mR 6 13mR 6 X 2R X

16 A black hole is an object whose gravitational field is so strong that even light cannot escape from it To what approximate radius would earth mass 5 98 x 1024 kg have to be compresed to be a black hole AIPMT 2014 1 10 9 m 3 10 2 m 2 10 6 m 4 100 m

4 The co ordinates of centre of mass of particles of mass 10 20 and 30 gm are 1 1 1 cm The position co ordinates of mass 40 gm which when added to the system the position of combined centre of mass be at 0 0 0 nd HmLare 1 3 2 3 2 3 2 3 3 4 3 4 3 4 2 3 2 3 2 3 2 4 3 4 3 4 3 4

1 0 5 3 0 25 4 0 75 A ball collides with an fixed inclined plan of inclination 0 after falling through distance h If it moves horizontally just aft the impact the coefficient of restitution is 1 tan 0 3 tan 0 2 cot 0 4 cot 9

3 9 m s 4 zero 3 A ball of mass M moving with speed V undergoes a head on elastic collision with a ball of mass nM initially at rest The fraction of the incident energy transferred to the second ball is 1 3 n 1 n 2n 1 n 2 4 n 1 n 4n 1 n 6

A bowler throws a ball horizontally along east direction with speed of 144 km hr The batsman the ball such that it deviates from its initial direction of motion by 74 north of east directio 1 kg and time of contact between bat and ba without changing its speed If mass of the ball is 3 0 02 s Average force applied by batsman on ball is A 800 N 53 East of North C 800 N 53 North of West B 800 N 53 North of East D 800 N 53 West of North

A 50 kg boy runs at a speed of 10 m s and jumps onto a cart as shown in the figure The cart s initially at rest If the speed of the cart with the boy on it is 5 m s then mass of the cart is 10k find k Assuming friction is absent between cart and ground 10m s V 0 5m s

Three particles of masses 0 5 kg 1 0 kg and 1 5 kg are laced at the three corners of a right angled triangle of ides 3 0 cm 4 0 cm and 5 0 cm as shown in the Fig 65 Locate the centre of mass of the system 1 5kg 3cm 0 5kg 5cm 4cm Fig 1 65 1kg 1 3 cm 1 5 cm

27 21 1 A block of mass 0 50 kg is moving with a speed of 2 00 ms on a smooth surface It strikes another mass of 1 00 kg and then move together as a single body The energy loss during the collision is AIEEE 08 a 0 16 J b 1 00 J 11 c 0 67 J d 0 34 J mot oxplodes and breaks into three fragments of masses in

There is a thin uniform disc of radius R and mass per unit area o in which a hole of radius R 2 has been cut out as shown in the figure Inside the hole a square plate of same mass per unit area o is inserted so that its corners touch the periphery of the hole Find centre of mass of the system R R 2

H A uniform symmetric solid pyramid with hexagonal base has height H Height of com from base is X Find x

4 A shell of mass 200 gm is ejected from a gun of mass 4 kg by an explosion that generates 1 05 kJ of energy The initial velocity of the shell is AIPMT Prelims 2008 1 120 ms 1 2 100 ms 1 3 80 ms 1 4 40 ms 1

E 32 As per this diagram a point charge q is pla the origin O Work done in taking another point charge Q from the point A Coordinates 0 a to another point B Coordinates a 0 along the straight path AB is 1 Zero A X AIPMT Prelims 2005 B 2 2 qQ 1 4 a 2 2a 36 37

Five homogeneous bricks each of length L are arranged as shown in by L 5 Find the x coordinate of the centre of mass relative to the origin O shown X ing of radius 2R made of same material having atro of mass of the

A projectile is fired from ground with velocity u at an angle 0 with horizontal At the highest point of its trajectory it splits up into two fragments of equal masses One part returns back via sante path to the point of projection Then the distance of the point where second part hits the horizontal from point of projection is 1 u sin 20 g 2u sin 20 2 1 u sin 20 2 9 u sin 0

ts choose the one best describes the two Statements Statement I A point particle of mass m moving with speed v collides with stationary point particle of mass then f M If the maximum energy loss possible is given as Statement II Maximum energy loss occurs when the particles get stuck together as a result of the collision 1 Statement I is true Statement II is true Statement II is a correct explanation of Statement I 2 Statement I is true Statement II is true Statement II is a not correct explanation of Statement 1 3 Statement I is true Statement II is false 4 Statement I is false Statement II is true m M m JEE Main 2013 Distance of the centre of mass of a solid uniform cone from its vertex is zo If the radius of its base is R and IJFF Main its height is h then zo is equal to

Xp 2 Two light rigid rods each of length I are connected by a hinged joint A particle A of mass m is attached at the joint and two thin cylinders B of mass m and C of mass 2m are attached at the free ends of the rods perpendicular to the rods The assembly is held motionless with rods vertical and cylinders B and C touching each other on a frictionless horizontal floor as shown in the figure After the assembly is released the rods rotate the cylinders move apart and finally the particle A hits the floor Find velocity of the particle A when angle between the rods becomes 0 Ange 1 Sino Sin 0 16 costo 4

2 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 J 1 E 2 J 2m J

Look at the drawing given in the figure which has been drawn with ink of uniform line thickness The mass of ink used to draw each of the two inner circles and each of the two line segments is m The mass of the ink used to draw the outer circle is 6 m The coordinates of the centres of the different parts are outer circle 0 0 left inner circle a a right inner circle a a vertical line 0 0 and horizontal line 0 a The y coordinate of the centre of mass of the ink in this drawing is IIT JEE 2009 a a 10 c a 12 b a 8 d a 3

A small pendulum bob is released from rest with the string being horizontal The bob swings and collides elastically with another ball B of same mass Ball B is kept on edge of smooth table of height 1 m Consider motion of B until it hits the ground then the time of motion is more for A ball A C both have same time of motion B ball B D none of these A lm

The centre of mass of triangle shown in figure has coordinates 3 x h h 1 x 2 Y 2 elm y b W 5 N O b X b 2 x y 2 4 x h 3 h 2 3

Two spheres of same mass m are moving in opposite directions with speed v and 2 They 1 collide with coefficient of restitution e Loss 2 of kinetic energy of the system in the collision is 27 mv 8 27 mv 1 3 2 4 3 mv 8 3 mv

SS A trolley child of total mass 200 kg is moving with a uniform speed of 36 km h on a frictionless track The child of mass 20 kg starts running on the trolley from one end to the other 10 m away with a speed of 10 ms relative to the trolley in the direction of the trolley s motion and jumps out of the trolley with the same relative velocity What is the final speed of the trolley How much has the trolley moved from the time the child begins to run and just before jump

2 A hoop of radius r and mass m rotating with an angular velocity is placed on a rough horizontal surface The initial velocity of the centre of the hoop is zero What will be the velocity of the centre of the hoop when it ceases to slip roo a c 4 roo 109 3 b d ro

4 A firehose squirts 10 kg s of water against a flat plate The velocity of stream is 10 m s If water comes to rest against the plate find the average force on plate 1 10N 2 100N m 3 1000N 4 IN with acceleration a

In the HCI molecule the separation between the nuclei of the two atoms is about 1 27 1 10 m The approximate location of the centre of mass of the molecule distance from hydrogen atom assuming the chlorine atom to be about 35 5 times massive as hydrogen is 1 1 2 2 5 3 1 24 A 4 1 5

An explosion breaks a rock into three parts i horizontal plane Two of them go off at right ang to each other the first part of mass 1 kg mo with a speed of 12 ms 1 and the second par mass 2 kg moves with 8 ms 1 speed If the th part flies off with 4 ms 1 speed then its mass NEET 20 1 5 kg 3 17 kg 2 7 kg 4 3 kg

A proton of mass m collides with a heavy particle After collision proton bounces back with of its 4 9 initial kinetic energy Collision is perfectly elastic Find mass of heavy particle 1 5 mp 3 3 m 2 6 mp 41

A horizontal ring of radius r spins about its vertical axis with an angular velocity w in a uniform vertica magnetic field of magnitude B The emf induced in the ring is S 1 Zero 1 3 Bor 2 2 r Bw 4 Bwr

22 Two particles A and B of equal mass M are moving with the same speed v as shown in the figure They collide completely inelastically and move as a single particle C The angle 0 that the path of C makes with the X axis is given by JEE Main Online 2017 1 tan 1 3 tan 0 A Y 30 45 B 1 2 5616 X 250 3 2 3 tan 0 1 4 tan 0 3 2 1 2

explay 2 40 A ball of mass 3 kg collides with a wall with velocity 10 m sec at an angle of 30 and after collision reflects at the same angle with the same speed The change in momentum of ball in MKS unit is 1 20 30 3 15 4 45 Centre of Mass

The density of a linear rod of length L varies as p A Bx where x is the distance from the left end Locate the centre of mass xcm 3AL 2 BL27 3 2A BL

Which of the following potential energy curves can possible describe the elastic collision between two billiard balls r is distance between centre of balls and R is radius of balls pe V r 1 3 V r 2 R r 2 R r 2 4 V r V r o 2 R 2 R

g The centre of gravity of a hollow cylinder of mass 200 is 10 cm above its base If 500 g of water is poured into the cylinder the water level comes up to a height of 6 cm What will be the height of the centre of gravity of the cylinder containing water 5 cm