Center of mass and momentum Questions and Answers

The end A of a ladder AP of length 5 m kept inclined to a vertical wall is slipping over a horizontal surface with velocity of 2 m s when A is at a distance of 3m from the wall Velocity of C M at this moment is A 1 25 m s C 1 m s B 0 m s D 2 m s 2m s A 3m

8 Two blocks of masses 10 kg and 20 kg are placed on th X axis The first mass is moved on the axis by a distane of 2 cm By what distance should the second mass b moved to keep the position of the centre of mas unchanged

A stationary bomb explodes into two parts of masses 3 k and 1 kg The total KE of the two parts after explosion is 2400 J The KE of the smaller part is a 600 J b 1800 J c 1200 J d 2160 J

Lower surface of a plank is rough and lies over a rough horizontal surface Upper surface of the plank is smooth and has a smooth hemisphere placed over it through a light string as shown After the string is burnt trajectory of C M of sphere is A circle C straight line B ellipse D none of these 4 C

A uniform rod AB of length 1 m is placed at edge of a smooth table as shown in figure It is hit horizontally at point B from left If the magnitude of the displacement of the centre of mass in 1 s is 5 2 m the angular speed of rod is A 30 rad s C 10 rad s B 20 rad s D 5 rad s Table B A

Three identical spheres of mass M each are placed at the corners of an equilateral triangle of side 2 m Taking one of the corners as the origin as shown in the figure the position vector of the centre of mass is y 2 m OM C M A 3 1 1 i i j 2 m 2 m M X

Two balls are thrown simultaneously in air The of the centre of mass of the two balls while acceleration in air a depends on the direction of the motion of the balls b depends on the masses of the two balls c depends on the speeds of the two balls d is equal to g

A hungry 173 kg lion running northward at 72 8 km hr attacks and holds onto a 30 2 kg Thomson s gazelle running eastward at 58 2 km hr Find the final speed of the lion gazelle system immediately after the attack final speed m s

A particle of mass m is projected with velocity v making an angle of 45 with the horizontal When the particle lands on the ground level the magnitude of the change in its momentum will be 1 mv 2 2 zero 3 2 mv 4 mv 2

D Potential energy of particle of mass 2 kg oscillating on x axis is given as U x 2 2 10 The total energy of oscillation is 26 J Find the maximum speed of particle 1 4 m s 2 8 m s 3 13 m s 4 6 m s

A wedge free to move of mass M has one face making an angle a with horizontal and is resting on a smooth rigid floor A particle of mass m hits the inclined face of the wedge with a horizontal velocity v It is observed that the particle rebounds in vertical direction after impact Neglect friction between particle and the wedge take M 2m v 10m s tana 2 g 10m s 0 a Determine the coefficient of restitution for the impact a M b Assume that the inclined face of the wedge is sufficiently long so that the particle hits the face once more during its downward motion Calculate the time elapsed between the two impar

A sphere of diameter r is cut from a solid sphere 1 of radius r such that the centre of mass of remaining part be at maximum distance from original centre then this distance is 1 r 2 r 2 r 3 None of these

11 Which of the following statements are correct a Centre of mass of a body always coincides with the centre of gravity of the body b Centre of mass of a body is the point at which the total gravitational torque on the body is zero c A couple on a body produce both translational and rotational motion in a body d Mechanical advantage greater than one means that small effort can be used to lift a large load NEET 2017 1 b and d 21 h and c 2 a and b 4 c and d

6 There is a square caromboard of side a A striker is projected in hole after two successive collisions Assuming the collisions to be perfectly elastic and the surface to be smooth The projection of striker is angle of a cot 1 3 4 b cos 1 c sin 1 4 3 4 0 a

A disc of mass 10 g is kept floating horizontally by throwing 10 marbles per second against it from below If the mass of each marble is 5 g What will be velocity with which the marble are striking the disc Assume that the marble strikes the disc normally and rebound downwards with the same speed 1

8 Problem 7 While punga KIL folates his leg 4000 the mp jou he moment of merta of the leg is 3 5 kgm and its otational kinetic energy is 180 J Randomized Variables 1 3 5 kg m KE 1801 d 1 3 m 50 Part a What is the angular velocity of the leg in rad s sin cos tan cotan atan cosh Hints deduction per hist Hints remaining asin acos E sinh cotanh acotan tanh Degrees Radians Submit Hint H 7 89 4 5 6 1 2 3 0 I give up Feedback deduction per feedback Grade Summ Deductions Podratial Submissions Attempts rema Ce per attemp detaded view

3 A body at rest breaks into two pieces of equal masses The parts will move a in same direction c in opposite directions with equal speeds d in opposite directions with unequal speeds b along different lines

3 A carpenter has constructed a toy as shown in the figure If the density of the material of the spheres 10 times that of cone the position of the centre of mass the toy is given by 1 At a distance of 2R from O 2 At a distance of 3R from O 3 At a distance of 4R from O 4 At a distance of 5R from O O 2R 0 O 4R 2R

Consider the following two statements A Linear momentum of the system remains constant B Centre of mass of the system remains at rest a A implies B and B implies A b A does not imply B and B does not imply A c A implies B but B does not imply A d R implies A but A does not imply B

39 Two blocks of equal masses m are released from the top of a smooth fixed wedge as shown in the figure The acceleration of the centre of mass of the two blocks is A 1 g 3 3g 4 2 g 2 g 4 T B 30 m m 60 C

A bullet hits a block kept at rest on a smooth horizontal surface and gets embedded into it Which of the following does not change a linear momentum of the block b kinetic energy of the block c gravitational potential energy of the block d temperature of the block

A light rod of length has two masses m and m attached to its two ends The moment of inertia of the system about an axis perpendicular to the roc and passing through the centre of mass is 1 m m l 2 m m l 3 m m m m 1 4 m m m m

0 Mass is distributed uniformly over a thin square plate If two end point of a diagonal are 2 0 and 2 2 what are the coordinates of centre of mass of plate 1 2 1 2 2 2 3 1 0 4 0 1 1 The distance of the centre of mass of the T shaped plate from O is 1 7 m 8m 0 2 2 7 m 3 4 m 2m 3m om 3m

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

d 0 11 A horizontal turn table in the form of a disc of radius r carries a gun at G and rotates with angular velocity about a vertical axis passing through the centre O The increase in angular velocity of the system if the gun fires a bullet of mass m with a tangential velocity v with respect to the gun is moment of inertia of gun table about O is 1 myr a C 10 mr V b d 2mvr 10 mvr 210 G Fig 3 286

Top View Cart A is traveling east when it collides with cart B which is traveling north Cart A has a mass of 3 05 kg and eart B has a mass of 2 10 kg The two carts travel together as a single object on a horizontal surface at an angle relative to due east as shown above 13 In one trial the initial speed of cart A is 2 5 m s and the initial speed of cart B is 1 5 m s The angle relative to east that the carts travel after the collision is most nearly B 36 C 45 E 62 14 In another trial the speed of the earts immediately after the collision is 0 60 m s and the earts slide 0 24 m on the horizontal surface before coming to rest The coefficient of kinetic friction between the sliding carts and the surface is most nearly A 0 08 B 0 13 C 0 19

5 77 a Four identical planks each of lengths L are arranged one above the other over a table as shown Each projects a distance a beyond the edge of the one that is below it What is the maximum possible value of a for the

A of mass m initially at rest height of 1 25 m on a frictionless ramp collides with and sticks to an identical particle B of mass m at rest as shown in the figure 1 25 m m OA B m 2m Then particles A and B together collide elastically with particle C of mass 2 m at rest The speed of particle Cafter the collision with combined body A B would be Take g 10 ms 2 a 2 ms b 1 25 ms c 2 5 ms d 5 ms

36 Figure 8 E4 shows a particle sliding on a frictionless track which terminates in a straight horizontal section If the particle starts slipping from the point A how far away from the track will the particle hit the ground 1 0 m A Figure 8 E4 0 5 m 1

Problem 7 4 When n number of particles of masses m 2m 3m nm are at distances x 1 x 4 x3 9 xn n units respectively from origin on the x axis then find the distance of their centre of mass from origin m 1 2m 4 3m 9 nm Sol x subtracting the above equations Xcm Xcm Ax cm m x x m x x m m m 4x m 4x m m

nm Problem 7 3 When n number of particles of masses m 2m 3m nm are at distances x 1 x 2 x 3 X n units respectively from origin on the x axis n then find the distance of centre of mass of the system from origin X2 intially and later respectively y axis 3 0

Problem 7 2 When n number of particles each of mass m are at distances x 1 x 2 x3 3 x n units from origin on the x axis then find the distance of their centre of mass from origin Problem 7 6 Two blocks of masses 10 kg and 30 kg are placed on x axis The first mass is moved on the axis by a distance of 2 cm right By what distance should the second mass be moved to keep the position of centre

atom at rest After collision the neutron is scattered at right angles to its initial direction of motion What could be the highest energy left over with the helium a

A ball of mass 10 kg hits a smooth horizontal surface with a speed of 10 2 m s at an angle of 45 as shown in the figure The coefficient of restitution between the ball and the surface is 0 5 and the ball remains in contact with the surface for 0 1 sec F is the instantaneous force exerted by the surface on ball at any time t during the collision A The speed with which the ball rebounds is 125 m s B During collision F may be less than or equal to 1800 N C During collision F may be greater than or equal to 100 N D The average force exerted by ground during collision is 1600 N 10 kg 10 2 m s 45 e 0 5

A ball of mass m is released from the top of an inclined plane of inclination 0 as shown It strikes 31 rigid surface at a distances from top elastically phr Impulse imparted to ball by the rigid surface is MNY gh 32 V 1 3 on a m gh 2 hen 0 4 Smooth ma h b m 3gh 2 V 2 V2

A foot baller kicks a football coming towards him at 10 m s such that ball comes to rest after kick Assume collision to be perfectly elastic and football to be light in comparison to the foot of man What is the speed of foot when football strikes the foot 0 10 m s 25 m s 05 m s

A ball is projected with velocity u 20 m s at an angle 60 to the horizontal towards a massive wall which approaches the ball with velocity u 7 m s After collision the ball retraces its path to the point of projection The coefficient of restitution between the ball and the wall is 3 10 k Find the value of k

The collision in which the relative velocity of approach before collision is equal to relative velocity of separation after collision is Completely inelastic collision Elastic collision Inelastic collision Both elastic and inelastic collision

4 0 m s M Before Jump After Jump 9 As shown in the figure above a child of mass 20 kg who is running at a speed of 4 0 m s jumps onto a stationary sled of mass 5 0 kg on a frozen lake The speed at which the child and sled begin to slide across the ice is most nearly A 0 20 m s B 0 80 m s C 1 2 m s D 3 2 m s T

Find the accelerations a a as of the shown in figure 6 E8 if a horizontal force of 10 N is applied on a 2 kg block b 3 kg block c 7 kg block Take g 10 m s M 0 2 2 0 3 H3 0 0 2 kg 3 kg 7 kg Figure 6 FS a1 a2 83

An object of mass 3 kg moving with a velocity of 5 m s along the positive X direction breaks up by itself into three equal mass fragments Two of them moves along the direction that are exactly opposite to each other with a speed of 2 m s each Find the speed of the third fragment OR Three concurrent forces Fi is equals to F Fil F F J and Facting simultaneously on particle to keep it in equilibrium draw a diagram to show how Fs can be found

Two point masses are connected by a light inextensible string are lying on a frictionless surfa MOITTOON shown in figure An impulse of magnitude 10 kg m s is given to 5 kg block 10 kg 60 5 kg 10 kg m s A Velocity of 10 kg block immediately after impulse is given m s B Velocity of 10 kg block immediately after impulse is given 2 m s C Speed of 5 kg block immediately after impulse is given d of 5 kg block immediately after impulse is given 28 28 9 m s m s

Two container A and B are partly filled with water and closed The volume of A is twice that of B and it contains half the amount of water in B If both are at same temperature the water vapour in the container will have pressure in the ratio of 1 1 2 2 1 1 3 2 1 4 A

30 Consider a large block placed on a smooth horizontal surface with a man standing at one end of the block The man walks to the other end relative to the block The distances absolute moved by the man and the block are a In the inverse ratio of their masses b In the direction ratio of their masses c Independent of their masses d Dependent both on their masses and speeds 36 In a gravity 37 height h abov down with a distance of th a h 1 m b h 2 m c 2h d a funct

26 When an explosive shell travelling in a parabolic path under the effect of gravity explodes in the mid air the centre of mass of the fragments will move a vertically downwards b along the original parabolic path c vertically upwards and then vertically downwards D horizontally followed by parabolic path adios

these 20 A disc of radius r cm of uniform thickness and uniform density o has a square hole with sides of length r 1 cm One corner of the hole 2 is located at the centre of the disc and centre of the hole lies on y axis as shown Then the y coordinate of position of centre of mass of disc with hole in cm is a r 2 14 r b d YA 0 r 4 14 3r 4 14 mass of the system will a u v c v 26 When an explosive she under the effect of gra centre of mass of the f a vertically downwa b along the original c vertically upwar d horizontally foll 27 The velocity of th 41 m s to v mass of the system on the system is a 25 N

Two blocks of equal mass m are tied to each other through a light string and placed on a smooth horizontal table One of the blocks is pulled along the line joining them with a constant force F Find the tension in the string joining the blocks ght line The

40 Match the following in Column I and Column II Assume radius as R and height of cone as le Column 1 Column II R A Distance of center of mass of this P 2 semicircular ring from centre B Distance of centre of mass semi circular disc from centre C Distance of centre of mass a solid R cone from vertex D Distance of centre of mass of hemi S spherical shell from centre 3R 4R 3n 2R It A B C D

A 500kg boat has an initial speed of 10ms as it passes under a bridge At that instant a 50kg man jumps straight down into the boat from the bridge The speed of the boat after the man and boat attain a common speed is 1 100 1 ms 2 11 10 11 ms 1 3 1 ms 4 ms 5 11 50 11

Example 4 5 A hammer weighing 5 kg descending from a height of 0 5 m struck a nail and stopped in second Find the force both in Newton and in kg wt exerted on the nail 1 10