‘PHYSICS F a ri i) e M ubgonanoo ‘foes 7 Plot eee - [MAIN + ADVANCED] ___ CENTRE OF MASS, ‘MOMENTUM & COLLISION — PERS Learning” : ey Tea (4 a)CENTRE OF MA: MOMENTUM & COLLISION ERCISE he © Four particles of mass 5, 3, 2;4 kg are at the points (1, 6). atithelte ‘centre of mass. 1, 5), (2, -3), (1, -4). Find the coordinates <4 6 The figure shows the postions and velocities of two particles. Ifthe = 3s icles move under the mutual attraction ofeach other, then find the == position of centre of mass at t= I s. Shaan A O46 Twogsts initially at rest are free to move in the x direction. Car A has mass 4 kg and car B has mass 2Xe, They are tied together, compressing a spring in between them, When the string holding them fogether is bumed, car A moves off with a speed of 2 m/s an \with what speed does car B leave #5 howrtiuch energy was stored in the spring before the string was burned. standing on a plank that has a mass of 150 kg. The plank, originally at rest, is free to Side ona frozen lake, which isa fla, frictionless supporting aire The girl begins to walk along the plank at a constant speed of 1.50 m/s relative to the plank. ¥af What is her speed relative to the ice surface? evan the speed of the plank relative to the ice surface? (QS Two balls of equal masses are projected upward simultaneously, one from the ground with speed m/sand other from a 40 m high tower with initial speed 30 mi. Find the maximum height attained by their centre of mass. ‘p Inthe arrangement shown in the figure, m, =2kgand m,=1 kg. String islightandinestesible. Find the acceleration of centre ofmassof > both the blocks. Neglect friction everywhere. P| A | QY Three carts move on a frictionless track with inertias and velocities as shown. The carts collide and stick together after successive collisions. 6 Find ioss of mechanical energy when B & Csstick together. (Q)4 Find magnitude of impulse experienced by A when it sticks to combined mass (B & C). m, = 2kg kg ms=2kg y= hms ims va= 2s ve Ae fee oc TTT TTT TTT TTT AGA body is thrown vertically upwards from ground with a speed of 10 m/s. Ifcoefficient of nof groynd, e= 1/2. Find oe the total distance travelled by the time it almost stops. \GYO time elapsed (after the ball has been thrown) when itis atits subsequent maximum height for the third time. GANGAL IARGES Pato Lid avrar Tower AO, oad Naw Kote05 | Page #21CENTRE OF MASS, MOMENTUM & COLLISION small block of mass2m rests at the bottom of a fixed circular, vertical track, which has a radius of R. The contact surface between the mass and the loop is frictionless, A bullet of mass m strikes the block horizontally with initial speed v, and remain embedded in the block as the block and the bullet circle the loop. Determine each of the following intgrms of m, vp, Rand g. co ‘The speed of the masses immediately after the impact. © 0 Tm 0. @F° Theminimum inital speed ofthe bullet ifthe block and the bullet are to successfully execute acomplete ride on the loop ohn spaceship is moving with constant speed v, ‘ne third ofits part with speed 2v, along + ° gravity free space along + Y-axis suddenly shoots out -axis, Find the speed of the remaining part. V ©A smooth sphere A of mass 0.1 kg is moving with speed Sm/s when it collides head on with another smooth stationary sphere B. If is brought to rest by the impact and e = ¥, find the mass of B, its speed justafier impact and magnitude of impulse during collision, LZ FON) © 4 A force F acts on an object (mass= | kg) which is intially atrestas shown s |. inthe figure. Draw the graph showing the momentum of the object varying during the time for which the force acts. 30100 wis) Ue 049" Bulletsofmass 10g each are fired fiom amachine gun at rate of 60 bulletsminute, The muzzle velocity of bullets is 100 m/s. The thrust force due to firing bullets experienced by the person holding the gun stationary is / QAFA 24-kg projectile is fired at an angle of 53° above the horizontal with an initial speed of —~_50mVs. Atthe highest point in its trajectory, the projectile explodes into two fragments of equal mass, the first of which falls vertically with zero initial speed. “© GY" Hoy far from the pointof firing does the second fragment strike the ground? (Assume the ground istevel) © WS How much energy was released during the explosion? wy ‘Two masses A and B connected with an inextensibe string of length /lieonasmooth 8 O ~~ horizontal plane. A is given a velocity of v/s alongthe ground perpendicular to line AB as shown in figure. Find the tension in string during their subsequent motion AL vi ‘ ~ Two trolleys A and B of equal masses M are moving in opposite directions with velocities 4 and => respectively on separate horizontal frictionless parallel tracks. When they start crossing each other, & ball of mass m is thrown from B to A and another of same mass is thrown from A to B with velocities all to ¥ . The balls may be thrown in following two ways: balls from A to B and B to A are thrown simultaneously. /_ballisthrown from A to Bafter the ball thrown from B reaches A. Which procedure would lead to a larger change in the velocities of the trolleys? BANSAL CLASSES Private Lid. ‘Gaurav Tower’, AiO, Road Not, IPIAy Kota0s | Page #22CENTRE OF MAS! MOMENTUM & COLLISION -A massive vertical wall is approaching a man ata speed u.. When itis at a distance of 10 m, the man ith speed 10 m/sat an angle of 37° which after completely elastic rebound reaches back directly into his hands , Find the velocity u of the wall . i ‘wo particles, each of mass m, are connected by a light inextensible string of length 2/. Initially they lie ona smooth horizontal table at points A and B distant apart. The particle at A is projected across the table wigh velocity u, Findshe speed with which the second particle begins to moye ifthe direction of u is, (Along BA, (B¥atan angle of 120° with AB, (e¥ferpendicular to AB. Ineach case calculate (in _—ferms of mand 1) the impulse of tension inthe string \ oO lass m, hts & sticks with m, while sliding horizontally with velocity v along the common line of centres “=~ of the three equal masses (m, =m, =m, =m). Initially masses m, and m, are stationary and the spring > AStnstretched. Find the velocities of m,,m, and m, immediately after impact. the maximum kinetic energy of m,, minimum kinetic energy ofm,. oO Frictions the maximum compression of the spring. Am)? £ no $ ob flexible chain has alength¢ and mass m. Its lowered on the table top with constant velocity v, Find the S&S, force thatthe chain exerts on the table as a function of time. (a) Q21 A carP is moVing with a uniform speed of 5(3') m/s towards a carriage of mass 9 Kg atrest kept on the rails ata point B as shown in fig. The height AC = (Wwe p@t — Fe? is 120 m, Cannon balls of 1 Kg are fired from the car with an initial velocity 100 m/satan angle 30? with the horizontal. The first canon ball hits the stationary attjm t Mo co carriage after atimett, and sticks to it, Determine ,. Att,, the second cannon ball is fired. Assume that the resistive force between the rails and the carriage, " is constant and ignore the vertical motion of the carriage throughout. If the , fae second ball also hits and sticks to the carriage. What will be the horizontal rote velocity of the carriage just after the second impact? Ta 229 Three ballsare keptona straight line ona smooth surface. The first bal is projected towards middle ball as shown, It collides with middle ball of mass m, which then collides with m,. We want m, to move with maximum possible velocity. What should bemass m. (in kg) Allcollision are elastic. [SINGLE CORRECT CHOICE TYPE] Aman of mass M standsat one end ofa plank of length L which lies at rest on a frictionless surface. The M ‘man walks toother end ofthe plank. Ifthe mass ofthe plank is, then the distance thatthe man moves relative to ground is 3L L L Az By Oo OF [E[BansAn GUnsees eiaee Ca Gaurar Tower ATO Rand WoT) TT Page # 23