Center of mass and momentum Questions and Answers

8 If linear mass density of a rod of length 3 m varies as 2 x2 then the position of the centre of mass of the rod is w r t to the end of the rod from where x is measure 1 1 m 3 1 5 m 2 2 4 m 4 1 95 m

understood how to solve it but why cant we use tota hange in momentum total time to calculate avg torque tried it that way but ans was wrong An automobile moves on a road with a speed of 54 kmh The radius of its wheels is 0 45 m and the moment of inertia of the wheel about its axis of rotation is 3 kg m If the vehicle is brought to rest in 15 s the magnitude of average torque transmitted by its brakes to the wheel is 1 6 66 kg m s 2 8 58 kg m s 2 3 10 86 kg m s 4 2 86 kg m s 2

7 A man of mass 50 kg is standing on a plank of mass 150 kg placed on a horizontal smooth floor If the man walks from end A to B then displacement of plank is 50 kg A 1 3 m to right 3 9 m to right 12 m 150 kg B 2 3 m to left 4 9 m to left

A billiard ball moving at a speed 2m s strikes an identical ball initially at rest at a glancing blow After the collision one ball is found to be moving at speed of 1 m s at 60 with the original line of motion The velocity of the other ball shall be 1 3 m s at 30 to the original direction 2 1 m s at 60 to the original direction 3 3 2 m s at 60 to the original direction 4 1 m s at 30 to the original direction

c 4 5 R d 7 5 R Distance of the centre of mass of a solid uniform cone fro its vertex is zo If the radius of its base is R and its height is the zo is equal to JEE Main 201 a c h 4R 5h 8 b d 3h 4 3h 8R

The figure shows the positions and velocities of two particles If the particles move under the mutual attraction of each other then the position of centre of mass at t 1 sis 1kg 5m s x 2m 3m s x 8n

Consider a gravity free hall in which a tray of mass M carrying a cubical block of ice of mass m and edge L is at rest in the middle the ice melts by what distance in m does the center of mass of the tray plus the ice system descend M m

A simple pendulum is suspended vertically from the ceiling of a car If the car is moving with an acceleration of 0 49 m sec the string of the simple pendulum will make an angle with the vertical whose magnitude will be 1 0 3 tan 1 2 2 tan 0 05 4 tam 3

An object comprises K two small identical disc as shown Which of the following can not be the centre of mass of the object RR 3 3 RR 3 2 R R RR R 2 X ring disc

A girl of mass 60 kg jumps with the horizontal velocity of 10ms1 onto a stationary cart with frictionless wheels The mass of the cart is 5kg What is her velocity as the cart starts moving Assume that there is no external unbalanced force working in the horizontal direction Options 4 65 ms 1 3 67 ms 1 9 23 ms1

Two bodies of masses 3kg and 9kg are moving with velocities 30 m s and 10 m s respectively along same direction collide with each other After collision they stick together and move with a common velocity in same direction Common velocity of system is ms 1 www E

Problem 83 A smooth semicircular wire track of radius R is fixed in a vertical plane One end of a massless spring of natural length 3R 4 is attached to the lowest point 0 of the wire track A small ring of mass m which can slide on the track is attached to the other end of the spring The ring is held stationary at point P such that the spring makes an angle 60 with the vertical The spring constant k mg R Consider the instant when the ring is released 1 Draw the free body diagram of the ring ii Determine the tangential acceleration of the ring and the normal reaction JEE 1996 C O 60 rictiona JEE 1997 wwwwwww

A skater of mass m is standing on ice throws a 6 stone of mass 2 m with a velocity v 5 ms in horizontal direction If the coefficient of friction between the skater and ice is 0 5 find the distance over which the skater will move take g 10 ms 1 20 m 3 10 m 2 15 m 4 5m v 5m s2 fe qui 0 5 t at a 1 20 m 3 10 m 8 fa fam 10 m s fag 2 15 m 4 5 m

A semicircular wedge of mass M is placed on a horizontal floor A man of mass m starts moving on the wedge from position A with constant speed v relative to the wedge Initially both man and wedge were at rest Neglect friction between the wedge and horizontal floor The man does not slip on wedge while moving from position A to C relative to wedge m A B M C

A rod of mass 2m and length L is resting on a smooth horizontal table Two identical particles each of mass m moving horizontally each with a velocity v strike the rod at the ends in directions perpendicular to the rod as shown in the figure and stick to it The angular momentum of the rod about the center of mass immediately after the impact is M L 292 A Zero B mvL 2 C mvL D 2mvL

Three identical balls are connected by light inextensible strings with each other as shown and placed over a smooth horizontal table Length of each string is 1 At moment t 0 ball B is imparted a velocity vo perpendicular to the string and then the system is left on its own The speed of A at the instant just before it collides with C is A C wo 8 2010 B I

ALLEN A particle of mass m collides head on with 19 another stationary particle of mass M such that the second particle starts moving and the first particle comes to rest after the collision Which of the following conditions is valid if the coefficient of restitution is e 1 e 0 m 3 e 1 M 2 e 4 2 m m 4 May SE VOR BY A Fal for 240x quid ZE au facciars a quiet fffff 1 e 0 m 3 e 1 M 2 e 4 e m m

ALLEN 6 A mass of 10 gm moving horizontally with a velocity of 100 cm sec strikes the bob of a pendulum and sticks to it The mass of the bob is also 10 gm The maximum height to which the system can be raised is g 10 m sec 1 Zero 2 5 cm 3 2 5 cm 4 1 25 cm A body is falling from height h It takes t seconds 7 100 10 atates 10 102 1 F 2 5 3 2 5 4 1 25 fra fermes I

ALLEN A uniform wire of length is bent into the shape 5 of V as shown The distance of its centre of mass from the vertex A is 1 8 2 3 1 3 8 A 60 B 2 LV3 4 None of these farger and arrit 1 8 2 3 Lv3 8 A 60 A 2 4 B 4 V 3

A body of mass m falls from a height h on 8 ground If it collides inelastically so that coefficient of restitution is e then the loss of energy in collision will be 1 mgh e 1 2 mgh 1 e 3 mgh 1 e 4 mgh e 1 I was the foreaft for f 1 mgh e 1 2 mgh 1 e 3 mgh 1 4 mgh e 1 e

A bullet weighing 10 gin and moving at 300 m s strikes a 5 kg ice block and drops dead The ice block is resting on a frictionless level surface The speed of the block after the collision is A 6 cm sec B 6 m sec C 60 cm sec D 60 m sec

2 Three identical thin rods each of mass m and length are joined to form an equilateral triangular frame The moment of inertia of the frame about an axis parallel to its one side and passing through the opposite vertex is 1 5 2 me2 3 3 ml 2 2 4 5 4 ml 5 3 ml

5 The centre of mass of a non uniform rod of length L whose k x mass per unit length a varies as where k is a L constant and x is the distance of any point on rod from its one end is from the same end 3 1 2 1 L 4 k 3 2 4 114 L 3 k

6m s Iron block 2 5kg 2 5m s magnetic block 1 2 m s 2 4 25 m s BEO 5 mic 3 6kg In the above situation two bodies moving on a smooth surface collide head on and stick together The combined block system moves with an approximate speed of

A man of mass M walks on a plank of mass 2M and length L Horizontal surface is smooth When the man reaches the other en of the plank he is at a distance from O equal to 7 2 034 5L 6 Plank Smooth 72

Two particles of masses 100 gm and 300 gm have at a given time velocities 101 71 3k 71 91 6k cm respectively Then velocity of centre of mass of the system in cms is a 34 31 15k b 151 34j 31k c 311 15 34k

9 A bullet of mass m moving with velocity vo k strikes the bottom of a stationary vertical uniform ring of same mass m and radius R 1m The ring lies in xy plane with its topmost point hinged on the ceiling The ring can rotate about x axis There is no friction between the hinge and the ring The bullet gets embedded in the ring immediately after collision Find the angular velocity of the system in radian s just after collision Take vo 11m s OL

Q 35 Which of the following is not an application of conservation of linear momentum a While firing a bullet the gun must be held tight to the shoulder b When a man jumps from a boat to the shore c A rocket explodes on midway from the ground d A body suspended from the hook of a spring balanced in a lift which is accelerated downward

Online Mock Test Series for NEET 2020 10 A man of mass m stands at one end of a plank of length L which lies at rest on a frictionless surface The man walks to the other end of the plank If the mass of plank is the distance m 3 that the man moves relative to the ground is 3 4 1 1 AL 2 4 14 L

A particle is thrown with velocity 20 2 m s as shown in figure It collides with inclined wall elastically and falls on ground at a point the x coordinate of which is 10xn metre then n is g 10 m s 20 2 m s 60m 45

9 In gravity free space a small ball is placed at the centre of a box of the same mass The ball and the box both are moving with a velocity v towards a wall Assume all collisions to be perfectly elastic a How many collisions are possible b Find velocities of the box and the ball and position of the ball relative to the box after all possible collisions

D connected by means of a pulley spring system on a smooth inclined plane of inclination as shown in the figure All the pulleys and spring are ideal Now B is slightly displaced from its equilibrium position It starts to oscillate Time period o oscillation of B will be Take m 4 kg K 5 N m 3 14 A B m

48 Particle A makes a perfectly elastic collision with another particle B at rest They fly apart in opposite direction with equal speeds If their masses are m m respectively then 1 2mA mB 2 3MA mB 3 4MA mB 4 3mA mB

2 Select 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

A bullet is fired from a gun The force on the bullet is given by F 600 2 10 t Where F is in newton and t in second The force on the bullet becomes zero as soon as it leaves the barrel What is the average impulse imparted to the bullet 1 9 N s 3 0 9 N s 2 zero 4 1 8 N s

A wedge of mass M rests on a smooth horizontal floor A block of mass m is kept on with a horizontal velocity v The height reached by the block after breaking off from the wedge is w r t initial velocity level Friction is absent O Mv 2 m M g 2Mv m M g m mv 2 m M g mv2 Ma Vel V M

0 Four particles of masses m m m3 and m4 are placed at the M2 M3 vertices A B C and D as respectively of a square shown The COM of the system will lie at diagonal AC if 1 m m3 A mi BM 2 m m4 3 m m 4 m m4 m3 m D m 3 C m x m3x me tona try to 2 mrtm 3

12 A rod of length 7 and mass m rotates about end A in vertical plane as shown Magnitude of normal reaction by the hinge at A is zoge A 1 mg 3 mg 4 l v M 2 4 mg 2 mg 3 E B L IN Ne n

A particle of mass m moving eastward with a speed v collides with another particle of the same mass moving northwards with same speed v The two particles coalesce on collision The new particle of mass 2m will move with velocity a North East c North West V b South West d 12 North East

A bullet of mass m moving horizontally with speed u meets a block of wood of mass M travelling along the same line but in the opposite direction with speed U and remains embedded in it Show that the loss of kinetic energy is of the form kMm where k is in terms of u U m M and find the loss in KE when the bullet of mass 20 g travelling at 400 m s hits a block of wood mass 4 0 kg moving at 2 0 ms

A non uniform bar of mass m is hung horizontally between two walls using two light ropes attached to the ends One of the ropes makes an angle 0 36 9 to the vertical and the other makes an angle 53 1 to the vertical If the bar is I 1 00 m long how far away from the closest edge is the centre of mass

A ball of mass 3kg and radius 3cm moving with velocity of 10m s collides obliquely with another ball of mass 2kg radius 2 cm kept at rest The impact parameter is 3 cm It is found that after collision the 3kg ball has a velocity component of 2 m s along the common normal Find the coefficient of restitution 3kg 3cm A C 1270 A 10m s B D 2kg 3839 B 213

A thin uniform rod pivoted at O is rotating in the horizontal plane with constant angular speedo as shown in figure A time t 0 a small insect starts from O and moves with constant speed v with respect to the rod towards the other end It reaches the end of the rod at t T and stops The angular speed of the system remains co throughout The magnitude of the torque 7 about O as a function of time is best represented by which plot Z A B C It T It V E F

A spherical water balloon is revolving at 60 rpm In the course of time 48 8 of its wa leaks out With what frequency will the remaining balloon revolve now Neglect all n conservative forces

1 A uniform semi circular disc of mass M and radius R lies in the X Y plane with its centre at the origin as shown in figure Also axis PQ is in the X Y plane Then match for the moment of inertia of semi circular disc about different axis P Ix Q ly R Iz S IPQ Column I 1 2 3 4 MR2 2 MR 4 MR2 4 MR Z Column II cos 0 P 2 cos 0 X

A particle of mass 4 kg starts to motion from rest with a constant acceleration 1 m s In the system there is another particle of same mass which is moving with a constant velocity of 2 m s Which among the following is not a possible value of the speed of COM after 2 s 2 m s 04 m s 01m s

particle of mass m 2 kg is projected along X axis with velocity V 5 ms It is acted on by a variable orce acting along Y axis as shown in figure What is the magnitude of its velocity at 2 sec in ms Fo 5N im 2 F X 3 1 sec

er Type Questions 10 Two point like objects of masses M and 4 M separated by distance 5r are freely released If they move under mutual gravitational force of attraction distance covered by lighter body before they collide is Nr Find the value of N 4

A cone of mass m and height H is completely filled with a liquid of same mass The height of centre of mass of the syster the base is OH 24 O 7H 24 O 5H 24 O 9H 24

Two identical dumb bells move towards each other on a horizontal smooth plane without having any angular speed as shown in the figure Each can be considered as two point masses m joined by a weightless rod of length 21 A light rod does not impart momentum perpendicular to its length Choose the correct options 34 B zero D v 2 V 5 The angular velocity of each dumb bell after elastic collision is A v l C 2v l B v 21 D 4v l m The velocity of the centre of mass of each dump bells after elastic collision is A v C 2v m 21 C