Center of mass and momentum Questions and Answers

A mass of 2 9 kg is suspended from a string of length 50cm and is rest Another body of mass 100g which is moving horizontally with a velocity of 150 m s strikes it After striking the two bodies combine together Tension in the string when it is an angle of 60 with the vertical is g 10m s 2 9 kg 50cm deman f 100g 150 m sed eu sud zaua tah ar zini aegu en uf c cala 60 g 10m s A 135N B 125N C 140N D 90N

Center of Mass 21 A sphere of mass m 2kg collides with a sphere of mass m 3kg which is at rest Mass m will move at right angle to the line joining centres at the time of collision if the coefficient of restitution is B 1 1 2 A 9 C 2 3 D 2 WIN

2 If a particle moves along a straight line whose equation is y mx then what will be its angular momen about the origin Explain your answer which are meshed together have radii of 9 50 cm and 0 15 cm The number of revolut

4 A thin uniform wire is bent to form the two equal sides AB and AC of triangle ABC where AB AC 5 cm The third side BC of length 6cm is made from uniform wire of twice the linear mass density of the first The distance of centre of mass from A is 34 11 34 11 34 9 A cm B cm C cm D 11 45 cm

7 A gun is mounted on a railroad car The mass of the car the gun the shells and the operator is 50 m where m is the mass of one shell If the velocity of the shell with respect to the gun in its state before firing is 200 m s what is the recoil speed of the car after the second shot Neglect friction

The moment of inertia of a metre scale of mass 0 6 kg about an axis perpendicular to the scale and located at the 20 cm position on the scale in kg m is Breadth of the scale is negligible EAMCET 2003 a 0 074 c 0 148 b d 0 104 0 208

An isosceles triangle is to be cut from one edge of a square lamina as shown in the figure such that the remaining portion when suspended from the apex P of the cut will remain in equilibrium in any position The value of his A C 3 3 2 2 2 e 2 B 3 3 e 2 D 2 2 e 2 P

energy and t is time The dimension of a and b is 1 ML T MLT 1 2 M L T M 1L T 3 3 M L T ML T 4 M 1L 2T3 M L T 31 A ball of mass m is moving with velocity u towards another stationary ball of mass 2m If collision is elastic then the percentage KE transferred by ball 1 to ball 2 is 1 68 8 3 88 8 2 78 8 4 100 32 A heavy solid sphere is thrown on a horizontal rough potent ak BED with initial velocity vo without rolling What motion

Example 9 17 Two thin uniform rings made of same material and of radii R and 4R are joined as shown The mass of smaller ring is m Find the MI about an axis passing through the centre of mass of system of rings and perpendicular to the plane A 0 4R

D A mass m moving horizontally along the x axis with velocity v collides and sticks to a mass of 3m moving vertically upward along the y axis with velocity 2v The final velocity of the combination is AIPMT Mains 2012 1 3v v 3 3 2 12 1v 1 1 0 4 1 2

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 100 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 3 b and c 2 a and b 4 c and d about

Two small balls having the same mass and charge and located on the same vertical at heights h and h are thrown in the same direction along the horizontal at the same velocity v The first ball touches the ground at a horizontal distance R from the initial vertical position At what height he will the second ball be at this instant Neglect any frictional resistance of air and the effect of any induced charges on the ground

A loaded spring gun of mass M fires a bullet of mass m with a velocity v at an angle of elevation 0 The is initially at rest on a horizontal smooth surface After firing the centre of mass of the gun and gun bullet system a moves with velocity b moves with velocity c remains at rest d moves with velocity M m vm M cos 0 in the horizontal direction v M m M m in the horizontal direction string passing over fixed pulley Assume

A thin rod of length L is lying along the x axis with its ends n mass length varies with x ask where n can be zero or any positive number If the position XCM of the centre of mass of the rod is plotted against n which of the following graphs best E 2008 approximates the dependence of XCM on n XCM 1 L L 2 L L 2 O XCM n 2 4 XCM L 2 XCM L L 2 O n n ular disc of radius R is removed from a bigger circular disc of radius 2R such that th ferences of the discs coincide The centre of mass of the new disc is aR from the centre ger disc The value of a is

0 A body of mass 2kg is froo to movo along x axis It is at rost at t subjected to a time dependent force F t in x direction The variation of F with time is as sh Haryana NTSE Stage 1 2 F 1 AN 0 2N 35 4 55 The change in momentum during journey is in N s A 4 50 B 7 50 C 5 06 D 14 06

Example 5 15 On a mine site a rock is exploded On explosion rock breaks into three parts Two parts go off at right angles to each other These two are 1 kg first part moving with a velocity of 12 ms and 2 kg second part moving with a velocity of 1 8 ms If the third part flies off with a velocity 4 ms what 11

7 A sphere P of mass m and velocity v undergoes oblique and elastic an collision with an identical sphere Q initially at rest The angle between the velocities of the spheres after the collision shall be

5 63 A straight thin uniform rod of length 4L and man 4M is bent into a square Its M I about one side is 1 5ML 2 7 ML 3 ML 48 4 ML 3

Example 8 22 A man of mass m is standing on a platform mass m kept on a smooth horizontal surface The man star moving on the platform with a velocity v relative to the platform Find the recoil velocity of platform

is rele and m m connected by a light spring of natural length is compressed completely and Two masses a quarter of the way tied by a string This system while moving with a velocity v along ve x axis pass through the origin at t 0 At this position the string snaps Position of mass m at time t is given by the equation 0 x t vt A 1 cosot Calculate i Position of the particle m as a function of time ii in terms of A UIT JEE 20031

7 Two balls one of mass m and other of mass 2 m are moving towards each other with respective speeds of 10 m s and 20 m s on a smooth horizontal floor If after collision they stick to each other and move as combined mass perfectly inelastic collision then the speed of combined mass will be NCERT Pg 129 1 20 m s 101 20 m s Ub 2 10 m s 4 50 m s

3 2 i 3j 5k 3 From the top of a tower of height 100m a 10 gm block is dropped freely and a 6gm bullet is fired vertically upwards from the foot of the tower with velocity 100ms simultaneously They collide and stick together The common velocity after collision is g 10ms 2 1 27 5ms 3 40ms 2 150ms 1 4 100ms

6 Two balls of equal mass are projected from a tower simultaneously with equal speeds One at angle 8 above the horizontal and the other at the same angle 0 below the horizontal The path of the centre of mass of the two balls is a a vertical straight line b a horizontal straight line d a straight line at angle a 0 with horizontal da parabola

he following table has 3 columns and 4 rows Based on table there are THREE questions Each uestion has FOUR options A B C and D ONLY ONE of these four options is correct 1 A ball of mass m moving with velocity vo in m Vo horizontal direction collides with a stationary ball of mass m line of impact makes an angle e with horizontal choose the correct option 1 11 III Column 1 Masses m m m m m m 3m 2m 3 1 m m m IV m m m 3m Column 2 Coefficient of restitution e 0 0 ii iii e 2 1 e T 3 iv For 8 0 which of the following is true A 1000 0 e 1 Column 3 Angle between final velocities of two balls P Q R S B P A zero r 2 r 3

Find the distance of centre of mass of the uniform rod of length into circular arc of radius R from the centre C as shown 3R B 2R A C T R TU D R TR if it is bent

A sphere of diameter r is cut from a solid sphere of radius r such that the centre of mass of remaining part be at maximum distance from orginal centre then this distance is 2 1 1 1 20 1 3 2 1135235 5 1 27 3 r 14 A 365 4 none of these

68 A metre stick weighing 240 g is pivoted at its upper end in such a way that it can freely rotate in a vertical plane through this end figure 10 E12 A particle of mass 100 g is attached to the upper end of the stick through a light string of length I m Initially the rod is kept vertical and the string horizontal when the system is released from rest The particle collides with the lower end of the stick and sticks there Find the maximum angle through which the stick will rise mahsin 37 2 m zg ml 1m M cose

A uniform rod of length L lies on a smooth horizontal table A particle moving on the table strikes the fod perpendicularly at an end and stops Find the distance travelled by the centre of the rod by the time it turns through a right angle Show that if the mass of the rod is four times that of the particle the collision is elastic 66

A mass of 1g carrying charge q falls through a potential difference V The kinetic energy acquired by it is E When a mass of 2g carrying the charge q falls through a potential difference V What will be the kinetic energy acquired by it a 0 25 E b 0 50 E c 0 75 E d E

A The position of centre of mass relative to body is independent of the choice of coordinate system R Centre of mass does not shift its position in the absence of an external force

D Consider a system of two particles having masses m and m If the particle of mass m is pushed towards m through a distance d by what distance should be particle of mass m be moved so as to keep the centre of mass of the system of particles at the original position 1 m d m m 3 d mid 2 m2 4 m2 d m

A is fixed point at a height above a perfect inelastic smooth horizontal plane A light inextensible string of length has c end attached to A and other to a heavy particle The particle is held at the level of A with string just taut and released from rest The speed of ball just after striking the plane is A 2 3 Select an answer A B 1 4gl 3 2gl 3 gl 5

A toy top of constant density do is constructed from a portion of a solid hemisphere of radius R with conical base of the height H The center of the spherical part is at the point where the top spins and the height of the conical base is equal to its radius r Find the moment of inertia of the top about its axis of symmetry HINT Take z axis for the axis of symmetry axis of rotation

An alpha particle of mass m suffers 1 dimensional elastic collision with a nucleus at rest of unknown mass It is scattered directly backwards losing 64 of its initial kinetic energy The mass of the nucleus is a 4m b 1 5m c 3 5m d 2m Canuary 2015

A proton of mass m collides elastically with a particle of unknown mass at rest After the collision the proton and the unknown particle are seen moving at an angle of 90 with respect to each other The mass of unknown particle is m m a m b 2m c d 3 2

Q A neutron having kinetic energy 12 5 eV collides with a hydrogen atom at rest Neglect the difference in mass between the neutron and the hydrogen atom and assume that the neutron does not leave its line of motion Find the possible kinetic energies of the neutron after the event

A uniform rod of length is suspended from one end and is made to undergo small oscillations What is length of a simple pendulum which has same time period as that of rod 2 4 1

A small sphere of radius R is held against the inner surface of a larger sphere of radius 6R The masses of large and small spheres are 4M and M respectively This arrangement is placed on a horizontal table as shown There is no friction between any surfaces of contact The small sphere is now released The coordinates of the centre of the large sphere when the smaller sphere reaches the other extreme position is A L 2R 0 JEE 1996 C 2R 0 B L 2R 0 6R M L O R 4M D 2R L 0

i A mass m is connected by a weightless cable passing over a frictionless pulley to a container of water whose mass is m at t 0 If the container ejects water in downward direction at a constant rate b kg s With a velocity v relative to the container determine the acceleration of m as a function of time 1 L m mo bt g br my mg bt m Figure 4 65

3 a A particle of mass m strikes elastically with a disc of radius R with a velocity v as shown in the figure If the mass of the disc is equal to that of the particle and the surface of the contact is smooth then the velocity of the disc just after the collision is m A 2v 3 B 2 R 2 m o C 3v 2 D v

A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor He throws a stone of 0 5 kg mass downwards with a speed 2 m s When the stone reaches the floor the distance of the man above the floor will be 1 20 m 2 9 9 m 3 10 1 m 4 10 m

Distance of the centre of mass of a solid uniform cone from it If the radius of its base is R and its height is vertex is ZO then Zo is equal to 5h 8 a c 4R b d 2 3h 8R 3h 4

MATCHING TYPE WITH 3 COLUMNS 4 ROWS he following table has 3 columns and 4 rows Based on table there are THREE questions Each question has FOUR options 4 B C and D ONLY ONE of these four options is correct 1 A ball of mass m moving with velocity vo in horizontal direction collides with a stationary ball of mass m line of impact makes an angle with horizontal choose the correct option 1 II III Column 1 Masses m m m m m m 3m 2m 3 1 m m m IV m m m 3m 0 ii Column 2 Coefficient of restitution e 0 iii iv For 0 0 which of the following is true A IV iv Q e e 1 2 1 3 e 1 m Vo Column 3 Angle between final velocities of two balls P R S R zero B 1 ii P D IV ii Q TC 2 T 3 Ji Q 70 V

Two men A and B are standing on a plank B is at the middle of the plank and A is at the left end of the plank Bottom surface of the plank is smooth System is initially at rest and masses are as shown in figure A and B start moving such that the position of B remains fixed with respect to ground and A meets B Then the point where A meets B is located at A the middle of the plank C the right end of the plank 40 kg A 60 kg B 40 kg 120 cm Smooth B 30 cm from the left end of the plank D None of these

3 The variation of density of a cylindrical thick and x long rod is P Po12 then position of its centre of mass from x 0 end is 1 2L 3 2 L 2 3 L 3 4 3L 4

ABCDECA is a planar body of mass m of uniform thickness and same material The dimension are as shown in the figure The moment of inertia of the body about an axis passing through poin A and perpendicular to planar body is I and that of about an axis passing through C an perpendicular to planer body is I Then choose the correct relation a AK E a B D a C a

Two particle of mass 4 kg 2kg are located as shown in figure then find out the position of centre of mass y 5m 4kg 37 0 0 2kg X

There is a uniform circular disc of radius R and a concentric disc of radius r where r R is cut off from it The distance of the new position of centre of mass of hollow disc from the centre of disc is O

3 50 W 4 60 W 13 If two bulbs of power 60 W and 100 W respectively each rated 110 V are connected in series with the supply of 220 V then 1 60 W bulb will fuse 3 Both bulbs will fuse 2 100 W bulb will fuse 4 Bulbs will not fuse constant voltage source

Question 15 The centroidal distance of a semicircle with R as its radius wrt its base is 4R 3 3R 4 3R 8 45R 3