Center of mass and momentum Questions and Answers

A sector cut from a uniform disk of radius 12 cm and a uniform rod of the same mass bent into shape of an arc arranged facing each other as shown in the figure If center of mass of the combination is at the origin what is the radius of the arc Your Answer

A bullet weighing 0 5 N and moving with a velocity of 400 m sec hits centrally a 30 N wood moving away at 15 m sec and gets embedded into it Find the velocity of bullet afte and K E lost

14 Two billiard balls A and B each of mass 50g and moving in opposite directions with speed of 5 m s each collide and rebound with the same speed If the collision lasts for 10 3 s which of the following statements are true a The impulse imparted to each ball is 0 25 kg ms and the force on each ball is 250 N b The impulse imparted to each ball is 0 25 kg ms and the force exerted on each ball is 25 x 10 5 N c The impulse imparted to each ball is 0 5 N s d The impulse and the force on each ball are equal in magnitude and opposite in directions

A Zener diode having breakdown voltage equal to 15V is used in a voltage regulator circuit shown in figure The current through the diode is o www 25092 1 5 MA Question Type Single Correct Type 2 10 MA 20V 3 15 MA 15V 1kQ

3 A uniform thin rod of length 2L is bent at right angles at a distance L from one end as shown in figure If length of rod is 1 8 m find the coordinate and position vector of the centre of mass of the system 2L

two particles of mass M1 and M2 and velocities U1 and U2 aU1 makes an elastic head on collision and the initial Kinetic energies of these two particles are equal and M1 comes to rest after collision then what is ratio of masses and velocities Two masses 2m and m are connected by an inextensible light string The string is passing over a light frictionless Pulley The mass 2m is resting on a surface and mass m is hanging in the air A particle of mass m strikes the mass m below from with velocity v0 and stick to it In another case a particle of mass m strikes the mass m with a velocity v0 from top and stick to it Calculate the ratio of velocities of mass m just after the collision in the first and second case

A semicircular wedge of mass M is placed on a horizontal floor A man of mass m starts moving on wedge from position A with constant speed v relative to the wedge Initially both man wedge were at rest Neglect the friction between wedge horizontal surface and man doesn t slip on the wedge while he moves from A to C relative to wedge The correct statement is 201 1 speed of wedge will first increase then decrease speed of the wedge winmain constant Page 2 2 3 speed of the wedge fir i 4 the wedge doesn t move upto a Zaximum value and then remains constant 71

A block of mass 2kg is placed in front of spring with k 1 96x10 N m The spring is compressed 20 cm and then released from rest What is the maximum distance d will the block travel along the incline from lunching point to highest point if the surface is frictionless and the incline angle 0 30 0 300 Initial d 19 30 Final h

lock A of mass MA 1 kg is kept on a frictionless horizontal surface and attached by a light thread to another block B of mass MB 0 75 kg Block B is resting on the ground and thread and pulleys are massless and frictionless A sm nass m 0 25 kg moving with speed u 400 m s horizontally towards left sticks to the block A as shown in the figure Speed of block B in m s just after collision between the block A and bullet is x Then the value of x is u 400m s A Rm 3 4 kg

Two bodies travelling along the same line with a relative velocity of 2 m s undergo one dimensional elastic collision After collision their directions of motion remain unchanged During collision the graph of the force exerted by one body on the other versus time is as shown Find the value of F kN in the graph if the harmonic mean of the masses of the two bodies is 5 kg force kN time ms

QA uniform rod of mass m and length is fixed at one end released from horizontal position as shown in the figure The angular velocity of the rod when the rod makes an angle 60 with vertical is Hinged m 1 A B C D 3g 21 4g 31 2g 3g 7

Three particles of equal masses are placed at the corners of an equilateral triangle as shown in the figure Now particle A starts with a velocity v towards line AB particle B starts with a velocity V towards line BC and particle C starts with velocity v3 towards line CA The displacement of centre of mass of three particle A B and C after time t will be given if v V2 V3 A zero V V V3 3 V 3 3 V V V3 V3 B VII 2 3 C

1 A small ball of mass m suspended from the ceiling at a point O by a thread of length moves along a horizontal circle with a constant angular velocity w Choose from following the correct option s Option D A B C Angular momentum is constant about O Angular momentum is constant about C Vertical component of angular momentum about O is constant Magnitude of angular momentum about O is constant Rate this questio

The vector position of a 3 40 g particle moving in the xy plane varies in time according to r 31 3 t 2 t where t is in seconds and r is in centimeters At the same time the vector position of a 5 85 g particle varies as r 31 2 t 6 t a Determine the vector position in cm of the center of mass of the system at t 3 00 s cm b Determine the linear momentum in g cm s of the system at t 3 00 s g cm s P cm c Determine the velocity in cm s of the center of mass at t 3 00 s cm cm s d Determine the acceleration in cm s2 of the center of mass at t 3 00 s cm s e Determine the net force in N exerted on the two particle system at t 3 00 s

A ring of radius r is spun about a vertical axis with an angular velocity w in a horizontal plane A uniform magnetic field of magnitude B exist in the region in vertical direction The emf induced in the ring is Tu Bw Bro Zero

R A uniform of mass M 1kg radius 1m is moving towards right with velocity vs 20m s and having angular velocity wo 4rad s about the axis perpendicular to plane of the disc passing through centre of disc Suddenly top point of the disc gets hinged about a fixed smooth axis The angular velocity in rad s of disk about new rotation axis is