Center of mass and momentum Questions and Answers

5 20 The locus of all the points on the X Y plane about Will the moment of inertia of the rod along an axis parallel to z axis same as that about O is The rod is lying in XZ plane initially later mass samo A Straight line C Parabola Figure 5 94 B Circle D Ellipse

For identical spheres of mass 1 kg and radius 10 cm each are placed on a horizontal surface touching one another so that their centres are located at the corners of a square of side 20 cm What is the distance of their centre of mass from centre of any sphere a 5 cm b 20 cm c 10 cm d none of the above BCC BCC

Two ice skaters of mass 120kg and 200kg are initially hugging on a frictionless ice surface Ten seconds after they push off from each other they are 8 0m apart The distance moved by the skater of mass 200 kg is 1 3 0 m 2 4 0 m 3 5 0 m 4 6 0 m

4 99 Mass m hits m with inelastic impact e 0 while sliding horizontally with velocity v along the common line of centres of three equal mass as shown in figure 4 155 Initially masses m and m3 are stationary and the spring is unstressed Find m V Ans 0 m 2 Figure 4 155 a The velocities of m m and m3 immediately after impact b The maximum kinetic energy of m3 c The minimum kinetic energy of m d The maximum compression of the spring 2 20 m 6ooooooooooooo m3 a rem dur

A unit mass at position vector F 31 4j is moving with a velocity v 51 6j What is the angular momentum of the body about the origin a 2 units along z axis c 38 units along y axis BCECE 2006 b 38 units along x axis d 38 units along z axis

A point charge Q is fixed and another particle of charge q and mass mis projected from very large distance with velocity vo towards fixed charge particle along a line which is at a perpendicular distance d from the fixed charge The minimum separation of this particle with the fixed charge is given by k 1 Ich far de Q f 9 2 m u ch kuf c a render Mtada a duz yg tw H gyfa faz de cu i 377 vo 77 T fua fhu J i Fer7 3Tai B C kQq mv kQq mv d kQq mv 2 k d kQq mv Correct Answer 2 1 AT40 d

The centre of mass of system of particles does not depend on 1997 position of the particles relative distances between the particles masses of the particles Correct

4 7 Am 20 gm bullet pierces through a plate of mass M 1 kg and then comes to rest inside a second plate of mass M 2 98 kg as shown in figure 4 128 It is found that the two astic plates initially at rest now move with equal velocities Find the percentage loss in the initial velocity of the bullet when it is between M and M Neglect any loss of material of the plates due to the action of the bullet nis at locity me cical s in ock the tar ma U d to the M Figure 4 128 M

Consider a system of two particles having masses m and m2 If the particle of mass m is pushed towards the centre of mass of the particles through a distance d by what distance would be particle of mass m2 move so as to keep the centre of mass of the particles at the original position

Two persons of masses 55 kg and 65 kg respectively are at the opposite ends of a boat The length of the boat is 3 0 m and weighs 100 kg The 55 kg man walks up to the 65 kg man and sits with him If the boat is in still water the center of mass of the system shifts by 2012 3 0 m 2 3 m zero 0 75 m

A speed vo If he throws the ball while running with u at an angle 0 to the horizontal what is the speed effective angle to the horizontal at which the ball is in air as seen by a spectator NCERT Exemplar projected a tan b tan c tan Vo cos 0 u vo sin 0 Vo u COS 0 sin 0 Vo d tan Vo sin 0 u vo cose vo sin 0 vo cos u 7

int A on the rod AB has an acceleration of 5m s and a velocity of 6 m s at an instant as shown in figure The acceleration of the end B at the same moment is 80 80 m s aA 5 m s VA 6 m s 80 i m s 4 m O 5m B 40 im s X D 75 im s

n elastic balls are placed at rest on a smooth horizontal plane which is circular at the ends with radius R as shown in figure Th m 2 n 1 respectively Find the minimum velocity which should be imparted to the first ball c masses of the balls are m m 2 m 2 mass m such that the nth ball will complete the vertical circle If the initial velocity of the first ball is an 1 5gR find a 2 3 4 n

A truck is loaded with 2000kg of iron and another identical truck is loaded with 2000kg of cotton If both the trucks are to go on the same rough road with same speed chances of over turning of Options 1 Iron truck are more 2 cotton truck are more 3 both truck are same

A particle is moving along a straight line with increasing speed Its angular momentum about a fixed po on this line 1 Goes on increasing 3 May be increasing or decreasing depending on direction of motion 2 Goes on decreasing 4 Remains zero

A particle of mass m is made to move with a uniform speed Vo along the perimeter of a regular hexagon The magnitude of impulse applied at each corner of the hexagon is Question Type Single Correct Type 1 2mv sin 1 2 mv sin 1 3 mvo sin Im

5 63 A rod of mass m and length 2R can rotate about an passing through O in vertical plane A disc of mass m and radius R 2 is hinged to the other end P of the rod and can freely rotate about P When disc is at lowest point both rod and disc has angular velocity oo If rod rotates by maximum angle 0 60 with downward vertical then wo in terms of R and g will be all hinges are smooth A Im 9g V16R 1 g 3 4 Figure 5 119 B 3g V23R D none of these fi

A tennis ball with small mass m2 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 B h 2h h

Two men A B of masses 60kg and 40kg ar standing on a plank of mass 100kg which is kep on a smooth horizontal plane If A and E exchange their position then plank will shift B A 260 kg 1 1 m left 2 2 m right 3 zero 100 kg 10 m 240 kg

Two identical balls A B each of mass 2 kg radius R are suspended vertically from inextensible strings as shown Third ball C of mass 1 kg radius r 2 1 R falls hits A B symmetrically with 10 m s Speed of both A B just after the collision is 3 m s The speed of C just after collision is 3 m s The speed of C just after collision is 2 m s The impulse on mass C is 12 N cm The impulse on mass C is 12 N m A M R C M 1 kg M 2 kg Br 2 1 R

7 3 1 3 Two smooth spheres A and B of equal radius lie on a horizontal table A is of mass m and B is of mass 3m The spheres are projected towards each other with velocity in m s vectors respectively and when they collide the line joining their centres is parallel to the vector 1 j If the coefficient of restitution between A and B is find the speed of ball in m s A after impact 1 3

COMPREHI A pendulum bob has mass m The length of pendulum is It is initially at rest A particle P of mass m 2 moving horizontally along ve x direction with velocity 2ge collides with the bob and comes to rest When the bob comes to rest momentarily another particle Q of mass m moving horizontally along z direction collides with the bob and sticks to it It is observed that the bob now moves along a horizontal circle The floor is a horizontal surface at a distance 2 below the point of suspension of the pendulum 1 Tension in string immediately after the first collision is A 2mg B mg 3 Les mg D 2 The height of circular path above the floor is 3l A 2 5l C mg B 48 3 D data not sufficient 20 16

Two triangular plates of surface mass density o and 0 are joined together to form a rhombus of side a as shown y co ordinate of centre of mass is y co ordinate of centre of mass is 02 01 60 Clear Response 51 052 60 Titl X

Toppling of a Block over another after Collision A block A of mass 2m is placed on block B of mass 4m which in turn is placed on a fixed table Both blocks have same length 4d The coefficient of friction between table and block B is u and there is no friction between blocks A small ball of mass m moving at speed v elastically collides normally to block B as shown at a height d above the table Find minimum speed v for which block A will topple over block B A B

A uniform rod is released from rest in the horizontal position shown in the figure The value of x for which the angular acceleration at the time of release is a maximum is 00 www w X l C 12

Iwo spheres A and B of masses m and m2 respectively collide A is at rest initially and B is moving with velocity v along x axis After collision B has a velocity in a direction perpendicular to 2 the original direction The mass A moves after collision in the direction AIPMT Prelims 2012 1 0 tan 1 2 to the x axis 2 0 tan 1 2 3 Same as that of B 4 Opposite to that of B to the y axis

u VT Ques Boy and trolley are V 4 moving at 6m s initially 4 suddenly boy starts walking at 4m s w r t final state of trolley Find the final velocity of trolley 2 fnet 0 3 6 m s b 2 4 m s c 5m s d 0 60kg 4m s version 2 0 40kg 6ml 6m s

5 If an ellipse is rotated about X axis an ellipsoid is formed then the coordinates of the centre of mass of a solid uniform semi ellipsoid formed by rotating a quarter ellipse given by the x y equation 2 1 as shown in diagram is b 3a a B 8 y 2 0

20 A particle is moving with velocity equal to 0 4 m s is subjected to a constant acceleration of 0 15 m s for 2s in a direction perpendicular to initial direction of motion The magnitude of final resultant velocity is 1 0 3 m s 3 0 5 m s 2 0 6 m s 4 0 7 m s

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 40 kg starts running on the trolley from one end to the other 10 m away with a speed of 10ms relative to the trolley in the direction of the trolley s motion and jumps out of the trolley with the 25 same relative velocity The final speed of trolley is N Find the value of N

2 A small ball of mass m 0 270 kg is moving at a speed of 3 60 m s It strikes a stationary larger ball of mass m 0 550 kg After the collision the balls follow the path shown in the figure where a 27 0 and 3 51 0 What is the magnitude of the velocity of the smaller ball after the collision Neglect friction and rotational motion VIE FEEL FREE TRI 15 M B

12 An explosion breaks a 32 0 kg object initially at rest into three parts Part 1 has a mass m 5 50 kg and a velocity of 58 0 m s due west Part 2 has a mass m 5 10 kg and a velocity of 72 0 m s due north Find the directio of the velocity of part 3 south of east

10 The drawing shows a collision between two small balls Ball 1 has a mass of 145 g and is moving along the x axis with a velocity of 5 60 m s It makes a collision with ball 2 which has a mass of 218 g and is initially at rest After the collision the two balls fly apart with angles as shown in the figure below a 54 and 3 56 What is the magnitude of the velocity of ball 2 after the collision m s m 7 m B C X

2 A small ball of mass my 0 270 kg is moving at a speed of 3 60 m s It strikes a stationary larger ball of mass m 0 550 kg After the collision the balls follow the path shown in the figure where a 27 0 and 51 0 What is the magnitude of the velocity of the smaller ball after the collision Neglect friction and rotational motion NILF NE

A high speed photograph of a club hitting head of the club with a speed of 1 5 x 10 KN Photo Researchers Inc a golf ball is shown in the figure below The club was in contact with a ball initially at rest for about 0 0014 s If the ball has a mass of 55 g and leaves the ft s find the average force exerted on the ball by the club

C velocity of 6 25 m s to the east What is the resulting velocity of the truck e car and truck collide in an elastic collision After the collision the car bounces off with a b Assume the car and truck collide in an inelastic collision What is the resulting velocity of the combined wreckage V Now assume the car drives into a concrete barrier It comes to rest in 0 28 seconds i What is the car s initial momentum ii iii iv What is the car s final momentum f 11 m s A car mass 1 600 kg is driving What is the impulse of the car What is the force exerted by the wall If the time of impact was increased how would that change the impact force exerted by the wall Explain the physics behind this change

Two pieces of play dough hit each other inelastically What is the final velocity of the dough the first piece had a momentum of 0 750kgm s the second had a momentum of 0 850kgm s and their combined mass was 0 500kg 0 312 m s 5 00 m s 0 100 m s 3 20 m s THE TE MES

1 Using the Impulse Momentum Theorem Ft m V m Vel calculate the force required to stop the Self Driving Car Sedan during a collision with another vehicle using the values provided in your spreadsheet REMEMBER The values you are using are unique to you and are based on YOUR Student ID Svens Work

5 On a smooth frictionless surface a puck A with a mass of 0 100 kg is pushed towards a stationary 0 050 kg puck B to cause a head on collision The initial velocity of the puck A is 12 m s E After the collision the Puck B moves with a velocity of 14 m s E a Find the velocity of the puck 4 after the collision C 3 b Find the net force acting on the puck A if the collision takes 0 20 s C 3

6 Skater A with a mass of 72 0 kg is moving at 11 0 m s S when he collides with skater B with a mass of 42 0 kg moving at 14 0 m s E The collision is completely inelastic and the two skaters move off together after the collision Find the velocity of the skaters right after the collision C 6

3 A rectangular block of mass M and height a is resting on a smooth level surface A force F is applied to one corner as shown in the figure At what point should a parallel force 3F be applied in order that the block undergoes pure translational motion Assume the normal contact force a between the block and surface passes through the centre of gravity of the block a vertically above centre of gravity 3 a 2 b vertically above centre of gravity 6 c No such point exists F

the page A metallic wire has the shape of a square frame and is placed in the field as shown While the shape of the wire is steadily transformed into a circle in the same plane the current in the frame 1 is directed clockwise 2 does not appear 3 is directed counter clockwise 4 is alternating

A rod AB slides on a V shaped wire with speed v as shown such that at any time OA field in the region is perpendicular downwards and has strength B induced emf in the rod is 1 Zero 3Bvl 160 B 2 Bvl 4 Bvl 2 potential difference between B and D and cum

at an angle with horizontal At the highest point of its trajectory it splits up into two fragments of equal masses One part returns back via same path to the point of projection Then the distance of the point where second part hits the horizontal from point of projection is 1 3 u sin 20 9 2u sin 20 2 1 u sin 20 29 4 2 u sin 0 Wat 81 1 men as you fang 12 28 geven va fa W u sin 20 gaat er and 2u sin 20 fanfang af e fa a 1 u sin 20 2 g 4 2u sin 0 2

A 6 5 kg block is placed on a frictionless surface conneted to an unknowm mass and arranged as shown The unknown mass falls from rest a distance 2 4 m acheiving a speed of 4 m s a Determine the unkown mass b Find the tension in the string M

In the diagram shown no friction at Rotate contact surface Initially the spring has no deformation What will be the maximum deformation in the spring Consider all the strings to be sufficiently large Consider the spring constant to be K

to the box after all possible collisions A box of length 22 cm and mass 100 g rests on a horizontal frictionless floor A small bead of mass 10 g is placed at the centre of the bottom of the box There is no friction between the bead and the bottom of the box The bead is projected with a velocity 11 cm s parallel to the length of the box If all the collisions are perfectly elastic find displacement of the box in a time interval 60 s after the bead was projected

to ypane oll 19 Two spherical bodies of equal mass M revolve about their centre of mass The distance between FIGOSTH the centre of the two masses is r The angular momentum of each about their centre of mass is 63 DE esmeil elumnio trigil s of benjol p 1 2 GM ristyp to eu 2 GM rar m 3 erit to exineo erit riquorit gniazed zixs ns juods bow e13 elupibns 1 GM ruonio 3

5 18 A smooth uniform rod AB of mass Mand length rotates freely with an angular velocity in a horizontal plane about a stationary vertical axis passing through its end A A small sleeve of mass m starts sliding along the rod from the point A Find the velocity V of the sleeve relative to the rod at the moment it reaches the other end B Krotov Ans wol 1 3m M th m st th

11 Moment of inertia of a uniform rod of length mass m about an axis through one end at an angle 45 to rod is 2 3 2 mL 1 ovil Jovil grizasq alxs 6 1 Ayte all at only ali of het ed liw natemsibus 4 mL 3 ML 12 s to anth motinu a to mL STO namoM A 21061 Lo Sne sinoni V X L