What will be nature of motion ofcentre of и of an isolated system ?

Ans.The centre of mass of an isolated system external force acting on the system) will either be at rest or it must be moving with a constant velocity.

4. Define centre of mass for a system of n-particles. Prove that it moves with constant velocity, provided the system is not acted upon by any external force.

1. What do you mean by centre of mass of a system ? Obtain expression defining the centre of mass of a system of two particles. Prove that the centre of mass of a system moves with constant velocity in the absence of external force on the system.

5. Discuss the motion of centre of mass in the following systems :

(a)Earth-moon system revolving around the sun.

(b)The Indian club thrown by a player towards the other.

11. The distance between the centres of the carbon and
oxygen atoms in the carbon monoxide (CO) gas molecule
is T13x 10~¹⁰ m. Locate the CM. of the molecule relative
to carbon atom. [Ans.0-646 x 10~¹⁰ m]

2. The identical spheres А, В and C, each of radius R are placed touching each other on a horizontal table. Where is the centre of mass of the system located relative to the

[Ans i(AB + AC)l

4. Two mass of 0-8 kg and 1-2 kg are lying in XY plane at the locations, whose coordinates are (1, -2) and (-3, 4)

respectively. Find the coordinates of the centre of mass of
the system. [Ans. (-1-4,1-6)]

5. Three point masses of 0-5 kg, 1-5 kg and 25 kg are located in XY-plane at points (2, -3), (3,5) and (-4, -6) respectively. What are the coordinates of the centre of mass of the system. [Ans. (1, -2)]

6. Two masses m-, and m₂ constrained to move in a horizontal plane collide. Given that т_г = 85 g, m₂ = 200 g and initially щ = 6-48 cm s^_1 and tu = — 6-78 cm s^_1, find the velocity of the centre of mass. [Ans. - 2-83 cm s^_1l

7. Two point masses of 2 kg and 3 kg are moving along the same line with speeds 3 m s'¹ and 5 m s^_1 respectively. Find the speed of the centre of mass of the system, if both the masses are moving in (a) the same direction and (b) in opposite directions. [Ans. (я) 4-2 m s^_1 (b) - 1-8 m s^-1l