Centre of Mass 289 Round II (Mixed Bag) Only One Correct Option 6. Two balls each of mass m are palced on the vertices A 1. (n - 1) equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the positive vector of and placed at vertex C. The centreB of an equilateral triangle ABC of side 1 m. A ball of mass 2 m is of mass of this system from vertexA (located at origin) is centre of mass [NCERT Exemplar] m 1 a (a) n- 1 (b) - a (n - 1) 1 m, 1 m (6) -() (c) (n- 1) a (d) a m 1 m 2. A gas molecule of mass m strikes the wall of the container with a speed v at an angle 0 with the normal to the wall at the point of collision. The impulse of the gas molecule has a magnitude (a) m, -m 2 (b) 2m 2 -m, 13 (c) (d) m, m, 4 4 4 (a) 3mv (b) 2 mv cos 0 7. A neutron travelling with velocity u and kinetic energy K collides head on elastically with the nucleus of an atom of mass number A at rest. The fraction of (c) mv (d) zero 3. A body of mass M at rest explodes into three pieces, two of which of mass M/4 each are thrown off in mutually perpendicular directions with speeds of 3 ms-1 and 4 ms-l respectively. Then the third piece will be thrown off with a speed of its kinetic energy retained by the neutron even after the collision is 1- A (a) A +1, A +1 (b) A -1, A +1 (d) A A (c) A (a) 1.5 ms-1 (b) 2 ms-1 8. Three identical balls A, B and C are lying on a horizontal frictionless table as shown in figure. If ball A is imparted a velocity v towards B and C and the collisions are perfectly elastic, then finally (c) 2.5 ms-1 (d) 3.0 ms-1 4. A particle is projected with 200 ms, at an angle of 60. At the highest point it explodes into three particles of equal masses. One goes vertically upward with velocity 100 ms, the second particle goes vertically downward with the same velocity as the first. Then, what is the velocity of the third particle? C 6. (a) ball A comes to rest and balls B and C roll out with speed v/2 each (b) balls A and B are at rest and ball C rolls out with speed v (c) all the three balls roll out with speed v/3 each (a) 120 ms-1 with 60 angle (b) 200 ms-1 with 30 angle (c) 50 ms-1 vertically upwards (d) 300 ms-1 horizontally (d) all the three balls come to rest 5. From a unifrom disc of radius R, a circular section of R 9. In a two blocks system an initial velocity v (with respect to the ground) is given to block A. Choose the correct 6. R from radius is cut out. The centre of the hole is at statement. the centre of the original disc. Locate the centre of gravity of the resulting flat body. [NCERT] A Rough R (a) to the right of centre O Smooth R (b) to the right of centre O (a) The momentum of block A is not conserved (b) The momentum of system of blocks A and B is conserved (c) The increase in momentum of B is equal to the decrease (c) to the left of centre O 3 R (d) to the left of centre 0 6. in momentum of block A (d) All of the above 112