Center of mass and momentum Questions and Answers

7 Two boys are left in the middle of a frictionless floor A boy of mass 20 kg gives a blow lasting for one millisecond of 100 kN to the other He himself will move with a velocity of a 1 ms b 0 5 ms d 0 005 ms 1 c 0 01 ms Ahody of mass 1 kg moving on a smooth horizontal surface with velocity 5 ms is to be brought

2 Two block of masses m and m are connected with the help of a spring of spring constant k initially the spring in its natural length as shown A sharp impulse is given to mass m so that it acquires a velocity Vo towards fight If the system is kept on smooth floor then find a the velocity of the centre of mass b the maximum elongation that the spring will suffer k m m M Vo

Section F Collision 1 A particle moving with kinetic energy K makes a head on elastic collision with an identical particl rest Find the maximum elastic potential energy of the system during collision

A bomb is projected with a velocity of 5 m s at an angle 8 from the horizontal ground It explodes in two equal fragments at the maximum height One of the fragments comes to rest just after explosion Centre of mass of the fragments falls on the horizontal ground at a horizontal distance x from the point of projection Taking sino and g 10 m s2 the value of x would be 4 5 Ox 24m Ox 24m O x 2 4 m O None of these A

A block moving horizontally on a smooth su rface with a speed of 20m s Suddenly expl odes in the ratio 1 2 and lighter part move p erpendicular to initial direction of motion wit h 60m s then find the velocity and direction of motion of heavier part

135 B Speed of A just after the impulse imparted is Speed of B just after the impulse imparted is Speed of just after the impulse imparted is Speed of A just after the impulse imparted is 23 7m V10J 7m 28 28 37 7m

Bodies of masses 4Kg and 2Kg are attached at the ends of a massless rod The positions of 4Kg and 2Kg are position of centre of mass of the system is A 12i 8j 3 C 8 i 127 m 8 12j 3 8i 8j 3 m m 21 53 m m and 41 25 m Then the

7 Force F is acting on a particle of mass m as shown in the force time curve The change in momentum of the particle over the time interval of 0 to 8 s is F N 6 3 0 3 2 4 6 8 time s D

Q 3 a c A frizzy drink beverage bottle is kept on a balance and the cap is opened Will there be any change in the balance There will be no change weight will decrease b d weight will increase weight will initially crease then decrease

A rectangular plate of mass M of dimensions a x b is hinged along one edge The plate is maintained in horizontal position by colliding a ball of mass m per unit area elastically 100 times per second this ball is striking on the right half shaded region of the plate as shown in figure Find the required speed of the ball ball is colliding in only half part of the plate as shown It is given M 3 kg m b 2 m a 1 m g 10 m s 0 01 kg JEE 2006 6 184 b 2 XX a

A person of mass M is sitting on a swing of length L and swinging with an angular amplitude 0 If the person stands up when the swing passes through its lowest point the work done by him assuming that his centre of mass moves by a distance L is close to A Mgl B Mgl 1 0 C Mall1 8 YOU MARKED

Consider mass of Sun and Earth to be 2 1030 kg and 6 1024 kg respectively The distance between Earth and Sun is 1 5 10 1 m Calculate the center of gravity of Sun Earth system 450 km from the center of Sun 450 km from the center of Earth 450 000 km inside the Sun 450 km inside the Earth

questions A man of mass 60kg sitting on ice pushes a block of mass of 12kg on ice horizontally with a speed of 5 ms The coefficient of friction between the man and ice and between block and ice is 0 2 The distance between man and the block when they come to rest is g 10ms YOUR ANSWER CORRECT ANSWER IS 6 25 CYDIANATION 4 6 5

A particle of mass 1 kg has been thrown with init speed 20 m s making an angle 60 with th horizontal ground The angular momentum of t particle about point of projection when the projec is at the highest point is g 10 m s 1 150 kg m s 2 300 kg m s 3 Zero 4 100 kg m s

Body A of mass 4m moving with speed u collides with another body B of mass 2m at rest The collision is head on and elastic in nature After the collision the fraction of energy lost by the colliding body A is 1 3 1 9 4 9 2 4 8 9 5 9

V i m V i m2 m2 2 00kg Two masses collide in one dimension m1 6 00kg v1i 10 0 m s v2i 4 00 m s After the collision mass m1 has velocity of v1f 7 00 m s If the collision lasted for a time 0 025 seconds what is the average collision force acting on mass m2 during the collisi Answer in newtons

Level 9 Which of the following relations associated with Newton s second law ramains valid for all velocities dv dt C F 4 mv A F ma B F m D All of them

A particle at rest explodes into two fragments of masses m and m m m which move apart with non zero velocities If X and 2 are their de Broglie wavelengths respectively then O A 1 0 11 1 O 1 1 O Data Insufficient

A rod of length 4m is leaned against a wall as shown It is released from the position when 8 60 Tr end A of rod remains in contact with the wall and its end B remains in contact with floor as the r slides down The distance covered by the centre of rod by the time it hits the floor is A 4m

ROSI V00V tent de stingr AXE P etallic shell of mass M and radius R filled with water of mass M is set into pure rolling motion on a smooth ontal surface as shown in the above figure Now water is freezed suddenly and the ice sticks with the

A rigid ball of mass m strikes a rigid wall at 30 and gets reflected without loss of speed as shown in the figure The value of impulse imparted by the wall on the ball will be 30 30

If the net external force acting on the system of particles is zero then which of the following may vary 1 Momentum of the system 2 Kinetic energy of the system 3 Acceleration of centre of mass

A bod A of mass M while falling vertically downwards under gravity breaks into two parts a 3 body B of mass M and a body C of mass M 1 4 4 The centre of mass of bodies B and C taken together shifts compared to that of body A towards 1 Body C 2 Body B 3 Depends on height of breaking 4 Does not shift

D X masses are m 133 0g mg 228 0g mc 573 0g and mp 313 0g what are the coordinates of the center of mass if the origin is located at mass A Enter your x coordinate first followed nate t Answer Tries 0 10 is the moment of inertia about a diagonal axis that passes through masses B and D Answer Tries 0 10

1 The mass m collides elastically with mass M The period of oscillation and amplitude of resulting motion of M are respectively m M 1 2T k moooo M M 2mv K m MVK smooth E IM 2my IM m 2 2 m 2mv K m MVK

ABLE MASS SYSTEM Consider at any time t a system of mass m travelling with velocity v as shown After a small time dt let its mass become m dm and velocity v dv Here a small mass dm travelling with velocity u adds into this system of mass m F is the force on r due to an external agent For the system of m dm ext v dv m dm dm U m mdi at time t I Fe du du ext I I Impulse change in momentum Fext dt m dm v dv mv dmu dua at time t dt I 1

The moment of inertia for a uniform rectangular slab about an axis passing through its geometric centre and perpendicular to its plane is length b breadth M 12 1 b 6 M 1 2 5 4 25 0 MP 223 Mb

Assertion A If an electron and proton enter a magnetic field with equal momentum then the paths of both of them will be equally curved Reason R The magnitude of charge on an electron is same as that on a proton 1 Point 000 Both A and R are true and R is the correct explanation of A Both A and R are true but R is not the correct explanation of A A is true but R is false Ise and R is also false

A simple pendulum when reaches its maximum angular displacement of 60 from the vertical is hit by a bullet moving horizontally with velocity 200 m s The bullet comes out of the bob horizontally with velocity 100 m s Find velocity of the bob immediately after the bullet comes out Neglect loss of mass of the bob due to piercing by the bullet Mass of the bob is 10 times of that of the bullet bullet bob

The mass of a pigeon hawk is twice that of the pigeons it hunts Suppose a pigeon is gliding north at a speed of Up 24 2 m s when a hawk swoops down grabs the pigeon and flies off as shown in the figure The hawk was flying north at a speed of VH 34 6 m s at an angle 0 45 below the horizontal at the instant of the attack What is the birds final speed uf just after the attack Uf m s What is the angle of below the horizontal of the final velocity vector of the birds just after the attack 0 Hawk o VH up Pigeon north Up

one hereas B IS a equal base area and height are arranged as shown in figure A is a hollow uniform thin conical shell without base If centre mass of the system of two cones lies on the common base find the ratio of their masses MA MB O O A 3 4 4 3 H H MA MB

Two balls of mass 6 kg and 8 kg move towards each other with speed 35 m s and 28 m s If collision is perfectly elastic then speed of both ball respectively is A 37 m s 26 m s B 26 m s 37 m s C 7 m s 39 m s D 39 m s 7 m s

Two cones A and B of equal base area and height are arranged as shown in figure A is a solid uniform cone whereas B is a hollow uniform thin conical shell without base If centre mass of the system of two cones lies on the common base find the MA ratio of their masses AL H

A ball A moving with a speed of 99 ms collides directly with another identical ball B moving with a speed v in the opposite direction A comes to rest after the collision If the coefficients of restitution is 0 8 the speed of B lligion is

Two balls each of mass 2 kg one at rest undergar oblique collision If collision is perfectly elastic them the angle between their velocities after collision is 1 30 3 45 2 60 4 90

100 A bullet is fired from a gun with a velocity 30 m s at an angle of 60 with the horizontal direction At the highest point of its path the bullet explodes into two parts with masses in the ratio 1 3 The lighter mass comes to rest immediately Then the speed of the heavier mass is a do 50 a 55 30 5 3 e 55rod 045 60 s abast tegods ar argodt nog 28 g was gow 1 3 551 Bodroom Des 30050 30s gos 30od 24jo pas saja tyds ads 55got sa

An object of mass 2 93 kg moving with an initial velocity of 5 07 i m s collides with and sticks to an object of mass 3 00 kg wi an initial velocity of 3 13 m s Find the final velocity of the composite object 1 m s

A body of mass M and moving with velocity u makes a head on elastic collision with another stationary body of m If A m M then the ratio f of the loss of energy of M to its initial energy will be O f A A 1 O A A 1 f 0 1 UA A 1 4A A 1 Marks 4 1

DA A straight rod of length L extends from x a to x L a Find the gravitational force it exerts on a poin mass m at x 0 if the linear density of rod A Bx a Gm c A a BL Gm BL A a L 1 4 1 1 b Gm A 1 a a L d Gm BL A a BL

A projectile is thrown from a point O on the ground at an angle 45 from the vertical and with a speed 5 2 m s The projectile at the highest point of its trajectory splits into two equal parts One part falls vertically down to the ground 0 5 s after the splitting The other part t seconds after the splitting falls to the ground at a distance x meters from the point O The acceleration due to gravity g 10 m s 5 The value of t is

A water jet whose cross sectional are is a strikes a wall making an angle 0 with the normal and rebounds elastically The velocity of water of density d is v Force exerted on wall is 1 2 av d cose 2 aud coff 0 0 2 2 av d sin0 4 ayd cose

556 A rod of mass m and length is held vertically on a smooth horizontal floor Now it is released from this position find the speed of its centre of mass when it makes an angle with the vertical 3gL 1 Simo Ans 0 6g sin cose 2 1 3 sin 0 11

Semiconductor A Zener diode having Zener voltage equal to 10 V is used in a voltage regulator circuit as shown in figure If current through the diode is 2 mA Then value of resistance R is nearly R wwww 3 4 15 V 1 417 Q 3 31202 www 2 600 2 4 810 22 1 kQ So SX400 2 In the question 3 if the value of R is 400 92 then current through the diode nearly 1 5 mA 3 10 mA 2 2 5 mA 4 2 mA

A ball of mass m is attached to the lower end of a vertical string whose upper end is fixed An identical ball B moving with a velocity vo 6 m s at an angle 0 45 from vertical collides elastically with the ball A as shown The velocity of the ball B just after collision is A 5 m s B 4 m s C 3 m s D 2 m s A m 0 45 B m V 6 m s

A small ball of mass m starts its motion from height h as shown in figure undergoes head on elastic collision with stationary identical mass attached to end of string of length L The correct relation between h and L if mass m just complete the vertical circle about O h Om O Frictionless platform 5L 2 h h 2L 3L h 2 IL Om

Statement I Two particles moving in the same direction do not lose all their energy in a completely inelastic collision Statement II Principle of conservation of momentum holds true for all kinds of collisions

1 55 A positive charge Q is fixed at a point A Another positively charged particle of mass m and charge q is projected from a point B with velocity u as shown in the figure 1 459 The point B is at large distance from A and at distance d from the line AC The initial velocity is parallel to the line AC The point C is at very large distance from A Find the minimum distance in meter of q from Q during the motion Take Qq 4 mud and d 2 1 meter Q 1 1 1 B C d

Sir Ma am please explain just the last option how force is conservative here I had posted this as my query and exce pt for the required last option all other options are explain ed Sir Ma am how to say if the force is conservative or not ie the last option Aug 15 2021 4 20 23 PM Answered A particle of mass m is initially at rest at the origin It is subjected to a force and starts moving along the x axis Its kinetic energy K changes with time as dk dt rt where is a positive constant of appropriate dimensions Which of the following statements is are true The force applied on the particle is constant The speed of the particle is proportional to time The distance of the particle from the origin increases linearly with time The force is conservative

A ball falls vertically onto a floor with momentum p and then bounces repeatedly The coefficient of restitution is e The total momentum imparted by the ball to the floor is S p 1 e 3 p 1 e 2 1 e 2 p 4 1 e 1 e 1 e 1 e

R A spherical part of radius 2 bigger solid sphere of radius R Assuming uniform mass distribution shift in the centre of mass will b 17 RIN RI 7 R 2 R 2 is removed from R 14 R